Question

Olive and Johan participated in a 30 mile race. Usually, Olive takes 2 hours more than Johan to finish the race. If Olive doubles his speed, then he will take 1 hour less than Johan to finish the race.

What is Olive's speed (in miles per hour)?

• A. 7 miles per hour
• B. 6 miles per hour
• C. 8 miles per hour
• D. 5 miles per hour

Answer 1

The correct option is D 5 miles per hour

Let's assume the speed of Olive to be x miles per hour (mph).

Normally, Olive takes two hours more than Johan to complete the race.

$\text{So, time taken by Olive}=\frac{30}{x}\text{h}$

$\text{∴ Time taken by Johan}=\frac{30}{x}-2\text{h}$

Now, on Olive doubling his speed, time $\text{taken by him will be}=\frac{30}{2x}$

He will take 1 hour less than Johan.

On arranging the equation, we get:
$\frac{30}{2x}=\frac{30}{x}-2-1$

$\Rightarrow \frac{30}{2x}-\frac{30}{x}=-3$

$\Rightarrow \frac{30}{x}-\frac{30}{2x}=3\text{(on changing signs)}$

$\Rightarrow \frac{60-30}{2x}=3$

$\Rightarrow 6x=30\text{(on changing sides)}$

$\Rightarrow x=\frac{30}{6}=5\text{mph.}$

Thus, Olive's speed is 5 mph.