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JAMB Mathematics 2017 Paper

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Question : 21

Total: 44

A man covered a distance of 50 miles on his first trip, on a later trip he traveled 300 miles while going 3 times as fast. His new time compared with the old distance was?

three times as much
the same
twice as much
half as much

Solution:

Concept:

Use the relation

\text{speed} = \frac{\text{distance}}{\text{time}}

to compare the two journey times.

Explanation:

Let the speed on the first trip be

v

miles per hour.

Then the speed on the later trip is

3v

miles per hour.

Time for the first trip:

t_1 = \frac{50}{v}

hours.

Time for the later trip:

t_2 = \frac{300}{3v} = \frac{100}{v}

hours.

Now compare the new time with the old time:

\frac{t_2}{t_1} = \frac{\frac{100}{v}}{\frac{50}{v}} = 2

.

Thus, the new time is twice the old time.

Answer:

C. twice as much

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