Math New Drill (Level 1) : Velocity Running around a pond

It takes 12 minutes for Taro and 8 minutes for Jiro to run the surroundings of a pond 1 round. 

When they started from the same point to the same direction, every how many minutes is Taro passed by Jiro ?

Math New Drill (Level 1) : Velocity Distance between two points

I walked from A point to B point at 4 km/h and returned running at 8 km/h. 

The time of a round trip was 45 minutes. 

Find the distance between A and B.

Math New Drill (level 1) : Velocity Two persons run in the round running course

There is a running course of 3.2 km one round. 

Taro and Jiro run to the same direction three round from the same position. 

Taro began to run at 200 m/m and Jiro began to run at 240 m/m 3 minutes afterward. 

When Taro finished running one round, he stopped and drank water. 

While he was drinking water, he was passed by Jiro. 

Then, Taro began to run at 260 m/m, he caught up with Jiro 3 minutes afterward. 

Then, although Taro ran with the same speed as Jiro, when they finished running two round, Taro walked at 80 m/m. 

Furthermore, after that, Taro began to run at 200 m/m and finished running three round later than Jiro for 7 minutes and 10 seconds. 

Answer the following questions. 

(1) Find the time while Taro was drinking water. 

(2) Find the distance where two persons ran with the same speed. 

(3) Find the distance where Taro walked.

Math Problem (Level 1) : Three needles in a disk (D18)

There is a disk as shown in a figure and three needles which continue rotating with a fixed speed clockwise respectively around the center O of the disk. 

The time concerning a needle rotating one time is 5 minutes, 8 minutes, and 14 minutes sequentially from a long needle. 

All of three needles overlapped at a certain time. 

Find the time concerning all of three needles overlapping next. 

Math New Drill (Level 2) : Velocity Problem 7 TOYOEIWA-2008

One day when Taro left home toward the school, 7 minutes after his leaving his mother noticed the thing left behind of Taro. 

Although she pursued at the speed of 80 m/m immediately, she thought that she could not catch up Taro. 

Then she borrowed a bicycle at the house of Taro's friend which is on the way and kept pursuing. 

Although she took 3 minutes to borrow, she caught up with Taro just in front of the school gate. 

The way from the house to a school is straight and the distance is 1500 m. 

The graph below expresses the relation between the time after Taro leaves home and the distance of two persons. 

Answer the following questions. 

Noted that the speed which Taro walks, the speed which his mother walks, and the speed of the bicycle are constant respectively. 

(1) Find the speed which Taro walks at the speed per minute. 

(2) Find the distance from the house of Taro to his friend's house. 

(3) Find the speed of the bicycle at the speed per minute.

Math New Drill (level 1) : Velocity Measure Problem 2(4) TOYOEIWA-2008

When I run the distance where it takes 14 minutes to run at the speed of 18 km/h, at the speed of 120 m/m, find the time for me to take.

Math Problem (Level 1) : Walk around the pond (D3)

Taro of 50m walk per minute and Jiro of 30m walk per minute started at the same time in the same direction around a circular pond. 

When Taro who separated Jiro catches up with Jiro in five minutes, find the distance around this pond?

Math New Drill (Level 2) : Velocity SNJ00-0404-L2 Distance between home and station

Taro left the house for the station and Jiro left the station for the house simultaneously. 

Both of 2 people walked by a fixed speed respectively. 

The distance between two persons was 632 m 5 minutes after leaving and it was 112 m 13 minutes after leaving. 

Find the possible distances between the house and the station.

Math Problem (Level 3) : Hour hand, minute hand and second hand (DDD7)

Answer the following questions about the hour hand (short hand), the minute hand (long hand) and the second hand of the clock in 60 minutes from 10:10 to 11:10.

(1) Find the time when an hour hand and the minute hand overlap. 

The second only should answer using a fraction.

(2) Considering the case that any two of three hands do not have overlapped either among three hands, an hour hand, the minute hand and the second hand. 

In this case, the center of the clock is divided into three angles as shown in a figure.

Find the number of times that two angles become equal among these from the time when it is found at (1) until 11:10 and also find the last time when two angles become equal.

As for the time, the second only should answer using a fraction.

Math problem (Level 3) : Going back and forth two points (DDD6)

Taro and Jiro are going back and forth between A point and B point with a fixed speed respectively by the bicycle.

They turn up immediately at A point and B point without taking a rest.

Taro started from A point and Jiro started from B point at the same time.

They passed at the point of 7 km from A first.

They move forward and they passed 2nd time at the point of 6 km from B.

Answer the following questions.

(1) In case Taro is faster than Jiro, find the speed ratio of Taro and Jiro.

(2) In case Jiro is faster than Taro, find the speed ratio of Taro and Jiro.

Noted that if there are some answers to this question, answer all cases.

Math Prob;em (Level 3) : Two persons moving on an annular road(DDD4)

There is an annular road as shown in the figure passing along P point and Q point. 

The distance between P and Q is the same in a clockwise rotation or a counterclockwise rotation. 

Taro moves from P clockwise and Jiro moves from Q counterclockwise on the road. 

They leave simultaneously and continue moving by a fixed speed respectively. 

5 minutes after leaving, Taro and Jiro met for the first time at R point since they left. 

Taro moved 4 km after the 1st meeting and met with Jiro again at S point. 

The distance of S point and Q point is 1.2 km along the road. 

Answer each of following questions.

(1) Find the speed of Taro an hour.

(2) Find the distance of the shorter one along the road from P point of R point.

(3) Three kinds are considered as the distance between P and Q along the road and the speed of Jiro an hour. 

Find both of them in all cases. 

Math Problem (Level 3) : Three persons moving on a circular pond (DDD2)

A, B and C are in the surroundings of a circular pond as shown in a figure at equal intervals. 

They began to run at the same time in the direction of the arrow in a figure respectively with the same speed. 

When two of three persons meet, the two persons run with the speed same for opposite. 

Three person’s speed is 150 m/m. 

Answer the following questions.

(1) It took 10 minutes for A to meet B 2nd time from the start. 

Find the length of a round of the pond.

(2) Find the time for three persons to return the original position at the same time from the start. 

Moreover, find the sum total number of times with which two of three persons meet in the time.

Math New Drill (Level 1) : Velocity Problem 3 TOHO-2014

There are P point and Q point 720m away.

Taro and Jiro left P at the same time and made a round trip between P and Q.

Jiro reached P three minutes later after Taro reached P.

The ratio of speed of Taro and Jiro is 3 : 2.

(1) Find the speed of Taro in meter per minute.

(2) Find the time of minutes and seconds when two people passed each other after they left P.

Math New Drill (Level 2) : SNJ00-0405-L2 Two ships sound whistle

Two ship A and B are advanced face to face. 

The speed per hour of A is 36km/h and the speed per hour of B is 27km/h. 

A rang a whistle and B which heard A's whistle rang a whistle immediately. 

The whistle of B has reached A 17 seconds later after A rang a whistle. 

The speed of sound is set to 340 m per second. 

How many seconds later was it that B heard A's whistle after A rang a whistle?

Math New Drill (Level 1) : SNJ00-0403-L1 Average speed

I went back and forth between two places with the speed of 3 km per hour on the way and 5 km per hour back on the way. 

Find the average speed per hour of the round trip.

Math New Drill (Level 2) : Velocity Problem4 JOSAIKAWAGOE-2014

There are 12 points are put at equal intervals on the circumference of a circular truck as shown in Fig.1. 

Boy runs clockwise and girl runs counterclockwise with a fixed speed, respectively. 

Girl goes around a truck in 24 minutes and boy runs by double speed of the girl. 

For example when one boy and two girls begin to run from the location of Fig.2 at the same time, boy and girls pass each other once at each of P point and Q point before the boy reaches spot R for the first time. 

Thus boy and girls will pass each other twice all together. 

Answer the following questions. 

(1) One boy and two girls begin to run from the location of Fig.2 at the same time. 

How many times do they pass each other all together before girls go around a truck?　　

(2) Two boys and three girls begin to run from the points of Fig.3 at the same time. 

How many times do boys and girls pass each other at the point P all together before girls goes around a truck? 

(3) Two boys and three girls begin to run from the points of Fig.3 at the same time. 

How many hours and minutes later do they become to be the position of Fig.4 after started running? 

Noted that boys and girls passed each other 9 times at the point P all together after they begin to run until they become to the position of Fig.4.  

Math New Drill (Level 1) : Velocity Problem1(5) JOSAIKAWAGOE-2014

Taro runs 100m in 12 seconds and Jiro runs in 15 seconds.
Taro and Jiro ran 100m race.
When Taro did a goal, how many meters behind Taro did Jiro run?

Math New Drill (Level 1) : SNJ00-0408-L1 The time when angle between long hand and hour hand is 90 degrees

Clock A is delayed at a rate of 6 minutes to 1 hour. 
Clock B proceeds at a rate of 6 minutes to 1 hour. 

Both clocks are set at correct time of 1:00. 
The angle between the long hand and the hour hand of clock A became 90 degrees for the first time from 1:00. 
Then what time o'clock, minutes and seconds is clock B?

New Math Drill : Level 1 : Velocity Problem3 JISSENJOSHIGAKUEN-2014

2 people of Taro and Jiro did footrace (running race). 

When both of 2 people ran through 100m, Jiro did a goal 4 seconds later than Taro. 

Next when Taro started from the point 25m after Jiro, 2 people made the goal at the same time. 

Noted that 2 people start at the same time and run with a fixed speed respectively. 

(1) Express the speed ratio of Taro and Jiro in the ratio of the least integer. 

(2) How many m per second was the speed of Taro?

New Math Drill : Level 1 : Velocity Problem3 JOHOKUSAITAMA-2014

Taro moves on foot and Jiro by bicycle on the road from A point to B point where is 16 km away from A point. 

The speed Taro walks is 80 m per minute and the speed of the bicycle of Jiro is 200 m per minute. 

Jiro left 30 minutes later after Taro. 

Jiro passed Taro on the way and he rested for a while after he moved. 

When 10 minutes passed since he began to rest, he met Taro, so he began to move by the same speed again immediately. 

Taro did not take a rest and Jiro took a rest once to arrive at B point. 

(1) How many hours and minutes later did Taro arrive at B point after Jiro arrived? 

(2) How many km from A point did Jiro catch up with Taro? 

(3) How many minutes and seconds did Jiro moved until the time when he took a rest after passing Taro?