Question

Two cyclists, 45 miles apart, start riding towards each other at the same time……..

Answer 1

Given:

Two cyclists, 45 miles apart, start riding towards each other at the same time.

Required:

We need to write the equation using the given information and to calculate the speeds of two cyclists.

Explanation:

(a)

Let us consider r is the speed of slower cyclist.

Distance covered by slower cyclist,

$r\times3$

Distance covered by faster cyclist,

$2\times r\times3$

Total distance is 45 miles.

Now from this data, we can say that

$\begin{gathered} 2\times r\times3+r\times3=45 \\ 6r+3r=45 \\ 9r=45 \end{gathered}$

(b)

From part (a)

$9r=45$

By simplifying, we get

$\begin{gathered} r=\frac{45}{9} \\ r=5 \end{gathered}$

This is the Speed of the slower cyclist.

Hence speed of the faster cyclist is 2 times as fast as the slower cyclist.

Therefore, speed of the faster cyclist is

$\begin{gathered} =2\times5 \\ =10 \end{gathered}$

Final Answer:

(a)

$6r+3r=45$

(b)

The speeds of both the cyclists is 5 miles per hour and 10 miles per hour.