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 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 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 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?

Math New Drill : Level 2 : Velocity Problem4 ATOMIGAKUEN-2014

Between the mountain top and foot of 3600 m two cable cars of A and B is scheduled to be operated as graph below.
It takes 32 minutes for descent and 40 minutes for ascent for both cable cars and they advance with a fixed speed.



Answer the following questions.

(1) As scheduled, A and B left at the same time.
How many meters from the foot do 2 cable cars pass each other first?

(2) Since it took time for checking, B was late to start descending for 10 minutes.
How many meters from the foot do 2 cable cars pass each other first in this case?

(3) The place where 2 cable cars pass each other was the spot in the middle of the top and foot of the mountain.
Answer which cable car was late to start in this case.
How many minutes was it late for leaving?

Math New Drill : Level 1 : Graph of Velocity Problem4 KAMAKURAJOGAKUIN-2014

In order to go from a house to school, Hanako walks from the house to the bus stop first.
She takes a bus from there and walks again after she gets off the bus.
For a while after Hanako left the house, her mother noticed s thing left behind and ran after the same way by car.
Then both of them have arrived at school at the same time.
Below is the graph which showed time and distance between Hanako and her mother after Hanako left the house.
Speed Hanako walks and speed of the bus and the car are fixed respectively.
She did not wait for a bus at a bus stop.




Answer the following questions.

(1) Find the speed per minute Hanako walks and the speed per minute of the bus respectively.

(2) Find the distance from the house to the school.

(3) Find the speed per hour of the car.

Math New Drill : Level 1 : Velocity Problem3(3) KAMAKURAJOGAKUIN-2014

Train A at a speed of 1,200m per minute has begun to enter a certain tunnel.
Train B of 1,500m per minute has begun to enter at the opposite side eight seconds later.
The top of train A and B came across in the middle of the tunnel.
Train B completely left the tunnel one minute 17 seconds later after train A began to enter the tunnel.
Find the length of this tunnel and the length of train B.

Math New Drill : Level 2 SNJ00-0411-L2 Two trains passing each other

Two trains A and B are moving parallel in an opposite direction at a fixed speed respectively. 

Head of A and head of B passed each other exactly at P spot. 

6 seconds later tail end of A and head of B passed each other. 

Moreover 4 seconds later head of A and tail end of B passed each other at Q spot where it's 150 m away from P spot. 

Finally tail end of A and tail end of B passed each other at R spot where it's 78 m away from P spot to the direction where A is moving. 

Find the speed per second and the length of A and B respectively.

Math New Drill : Level 2 SNJ00-0407-L2 Moving sidewalk between station and park

There is a moving sidewalk which moves by a fixed speed between a park and a station. 

Taro went to the park by walking on this moving sidewalk from the station. 

Jiro went to the station from the park standing on the moving sidewalk. 

They have begun to move at the same time. 

When Taro walked 80 steps, they passed each other. 

When Taro walked 32 steps after passing, he arrived at the park. 

Jiro arrived at the station 60 seconds later after Taro's arrival. 

The stride of Taro's one step is 75cm. 

Find the speed per minute Taro walks and the speed per minute of the moving sidewalk. 

Math New Drill : Level 2 SNJ00-0409-L2 Graph of two train

Train A and B run with a fixed speed respectively. 

Fig.1 shows a relation between the time from when two trains meet until they get away and the length of the part of trains overlapping. 

Fig.2 shows a relation between the time from when A catches up with B until they get away and the length of the part of trains overlapping. 

Answer the following questions. 

(1) Find the speed per second of A. 

(2) Find the length of longer train.