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Math worksheet for Speed and Rate sums

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Speed and Distance sums

1) James cycles from town A to town B that was 50 km away. One hour later, Kelly also left town A for town B but she cycled at an average speed 10 km/h faster than James. Kelly caught up with James after cycling for 1 ½ hours.
i) Find the speed of Kelly.
ii) After Kelly caught up with James, how long would she need to cycle to reach town B?
iii) How far away from town B was James when Kelly completed her journey? (1 step only!)

Ans :- i) Kelly's speed was 25 km/h
ii) ½ h
iii) 5 km

2) Daniel and Timothy were driving from town A to town B at constant speed. They both left town A at the same time. Daniel speed was 100 km/h while Timothy's speed was 70 km/h. Daniel reached town B 67 hour before Timothy.
i. How long did it take for Daniel to drive from town A to B? )
ii. Find the distance between the two towns?

Ans :- i) 2 h
ii) 200 km

3) Ahmad drives from town A to town B. If his average speed is 60 km/h, he will reach town B at 12:30 pm. If his average speed is 70 km/h, he will reach town B at 12 pm.
Find the distance between the two towns.

Ans :- 210 km

4) James drives from town A to town B. If his average speed is 100 km/h, he will reach town B at 3 pm. If his average speed is 60 km/h, he will reach town B at 5 pm. Find his average speed if he wants to reach town B at 4 pm.

Ans :- 75 km/h

5) Gary and Henry went for a race. If Gary started running when Henry was 10 m ahead, Gary would catch up with Henry in 5 seconds.
If Gary started running 2 seconds after Henry, Gary would catch up with Henry in 4 seconds.
Find Henry's speed.
Find Gary's speed.

Ans :- Henry's speed is 4 m/s
Gary's speed is 6 m/s

6) Ahmad, Bob and Carl leave town A for town B at the same time.
Ahmad rides a motorcycle at a speed 60 km/h.
Bob walks at a speed of 4km/h while Carl jogs at a speed of 20 km/h.
Ahmad gives a lift to Bob from town A to travel a part of the journey and then he rides back to pick up Carl. All three of them arrive at town B at the same time. If Bob walks 2 km, how far does Carl jog?

Ans :- 14 km

7) At 10 am, Simon left town A for town B traveling at an average speed of 80 km/h.
At the same time, Peter left town B for town A traveling at a constant speed.
Some time later, Simon and Peter passed each other. At 1 pm, they were 60 km apart. Simon reached town B at 4 pm.
(i) Find Peter speed.
(ii) When would Peter reach town A.

Ans :- i) Peter's speed was 100 km/h
ii) Peter would reach Town A at 2.48 pm

8) Town A was 180 km away from town B.
John started out from A at 6:30 am driving at a uniform speed 75 km/h towards town B.
At the same time, Kelly left town B to go to town A.
Both cars passed each other at 7:50 am.
(i) At what speed was Kelly driving when she passed John's car?
(ii) At what time would John reach town B if he increased his speed by 5 km/h for the rest of the journey?

Ans :- i) 60 km/h
ii) 8.50 am.

9) At 12 pm, Janice left A for town B, while Tom set off from town B to town A. They passed each other at 3 pm. If Tom's average speed was 40 km/h faster than Janice's, find Tom's average speed. (90 km/h)

Ans :- 90 km/h

10) Town A and town B were 180 km apart. At 9 am, James left town A for town B while Henry left town B for town A. Both of them drove at uniform speed.
(i) If James drove at the same speed as Henry and they passed each other at 10:30 am. What was James' speed?
(ii) If James drove 10 km/h faster than Henry and they passed each other at 11 am, what was James' speed?

Ans :- i)60 km/h
ii) 50 km/h

11) A man took 5 h to travel from Town A to Town B. After travelling for 1½h at an average speed of 60 km/h, he took a rest and then continued to travel the remaining 210 km at an average speed of 70 km/h. Find his average speed for the whole journey and the time he spent to rest.

Ans :- His average speed is 60 km/h and ½ h he spent to rest .