Time, Speed, Distance & Work — Practice

Question 1

A car covers 180 km in 3 hours. Find its speed.

Accepted Answer

Speed $=180\div3=60$ km/h.

Answer: 60 km/h.

Question 2

A can complete a job in 20 days and B can complete the same job in 25 days. Working together, how many days will they take?

Accepted Answer

Combined rate $=\frac{1}{20}+\frac{1}{25}=\frac{5}{100}+\frac{4}{100}=\frac{9}{100}$ per day. Time together $=\frac{100}{9}\approx11.1$ days.

Answer: approximately 11.1 days.

Question 3

Two trains, 130 m and 170 m long, move toward each other at 60 km/h and 40 km/h. Find the time they take to cross each other.

Accepted Answer

Relative speed $=60+40=100$ km/h $=100	imes\frac{5}{18}\approx27.8$ m/s. Total length $=130+170=300$ m. Time $=300\div27.8\approx10.8$ seconds.

Answer: approximately 10.8 seconds.

Question 4

A train travelling at 70 km/h overtakes another train travelling at 52 km/h in the same direction. If their combined length is 250 m, find the time to overtake.

Accepted Answer

Relative speed $=70-52=18$ km/h $=18	imes\frac{5}{18}=5$ m/s. Time $=250\div5=50$ seconds.

Answer: 50 seconds.

Question 5

A boat travels downstream at 18 km/h and upstream at 10 km/h. Find the boat's own speed and the stream's speed.

Accepted Answer

Boat's speed $=\frac{18+10}{2}=14$ km/h. Stream's speed $=\frac{18-10}{2}=4$ km/h.

Answer: Boat = 14 km/h, Stream = 4 km/h.

Question 6

A person travels equal distances at 50 km/h and 75 km/h. Find the average speed for the entire journey.

Accepted Answer

$	ext{Average speed}=\frac{2	imes50	imes75}{50+75}=\frac{7500}{125}=60$ km/h.

Answer: 60 km/h (not the simple average of 62.5).

Question 7

A is thrice as efficient as B. Working together, they complete a job in 6 days. Find how long each would take working alone.

Accepted Answer

Let B's rate be $x$; A's rate is $3x$. Combined rate $=4x=\frac{1}{6}$, so $x=\frac{1}{24}$. B alone takes $24$ days; A alone takes $\frac{1}{3x}=8$ days.

Answer: A = 8 days, B = 24 days.

Question 8

An inlet pipe fills a tank in 12 hours; an outlet pipe empties the same tank in 18 hours. If both are opened together, how long does the tank take to fill?

Accepted Answer

Combined rate $=\frac{1}{12}-\frac{1}{18}=\frac{3}{36}-\frac{2}{36}=\frac{1}{36}$ per hour. Time to fill $=36$ hours.

Answer: 36 hours.

Practice — Time, Speed, Distance & Work

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