Question

Albert was challenged to a race by his friend Martin. Martin started running first, and Doug didn't start running until Matt had finished a quarter-mile lap. Albert overtook Martin exactly at their sixth lap. If both boys ran at a constant speed, with Albert running $2$ miles an hour faster than Martin, find the speed of Martin.

• A. $10.5$ miles per hour
• B. $10$ miles per hour
• C. $9$ miles per hour
• D. $8$ miles per hour
• E. $7.5$ miles per hour

Answer 1

Answer: (B)

$10$ miles per hour

Let the speed of Martin is $x$ miles per hour.

So the speed of the Albert is $x+2$ miles per hour.

Each lap is one quarter of mile, so Albert run $1.5$ mile and Martin run $1.25$ miles.

So the time that is taken by the Martin $=\frac{1.25}{x}$

Time taken by Albert $=$ $\frac{1.5}{x+2}$

Both take the same amount of time, so

$\Rightarrow \frac{1.5}{x+2}=\frac{1.25}{x}$

$\Rightarrow 1.5x=1.25(x+2)$

$\Rightarrow 1.5x-1.25x=2.5$

$\Rightarrow 0.25x=2.5$

$\Rightarrow x=\frac{2.5}{0.25}=10$

So the speed of martin is $10$ miles/hr.