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.

Step-by-step explanation:

(a)

Let us consider r is the speed of slower cyclist.

Distance covered by slower cyclist,

`r*3`

Distance covered by faster cyclist,

`2* r*3`

Total distance is 45 miles.

Now from this data, we can say that

`\begin{gathered} 2* r*3+r*3=45 \\ 6r+3r=45 \\ 9r=45 \end{gathered}`

(b)

From part (a)

`9r=45`

By simplifying, we get

`\begin{gathered} r=(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*5 \\ =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.