Question

two cyclist start from the same point and ride in opposite directions.One cyclist rides twic as fast as the other.In 2 hr they are 78 mi apart.find the rate of each cyclist

Answer 1

In order to find the speed of each cyclist, we will need to use the following equation:

`\text{distance}=\text{speed}\cdot\text{time}`

Let's call the cyclists A and B.

If the speed of cyclist A is twice the speed of cyclist B, we have that:

`\text{speedA}=2\cdot\text{speedB}`

After 2 hours, they are 78 mi apart, so using time = 2, the sum of their distances will be 78 (we use the sum because they are going in opposite directions. If they went in the same direction, we would calculate the difference of distances):

`\begin{gathered} \text{distanceA}+\text{distanceB}=78 \\ \text{speedA}\cdot\text{time}+\text{speedB}\cdot\text{time}=78 \\ \text{speedA}\cdot2+\text{speedB}\cdot2=78 \\ 2(\text{speedA}+\text{speedB)}=78 \\ 2(2\text{speedB}+\text{speedB)}=78 \\ 2(3\text{speedB)}=78 \\ 6\text{speedB}=78 \\ \text{speedB}=(78)/(6)=13 \end{gathered}`

The speed of cyclist B is 13 miles per hour.

The speed of cyclist A is:

`\begin{gathered} \text{speedA}=2\text{speedB} \\ \text{speedA}=2\cdot13=26 \end{gathered}`

The speed of cyclist A is 26 miles per hour.

A table showing the rate of each cyclist, the time and the distance traveled by each one is: