Question

Fernando took the train due south from the airport, heading to the end of the line. At the same time, Darrell also left home and started driving due north to the end of the line, where he would pick Fernando up. Fernando's train traveled 59 kilometers per hour, and Darrell drove 77 kilometers per hour. They started out 43 kilometers apart and arrived at the station at the same time. How long did it take them to meet?

Answer 1

Let the distance travelled by Fernando to the meeting point, station, be 'x'.

Given that the distance between Fernando and Darrell is 43 kilometers, the distance between Darell and the station is (43-x) kilometers.

The schematic diagram is given below,

Consider the following relation,

`\text{Time}=\frac{\text{ Distance Travelled}}{\text{ Time Taken}}`

Given that the time talen by Fernando to cover 'x' kilometers at 59 km/hr is the same as the time taken by Davell to cover '43-x' kilometers at 77 km/hr,

`\begin{gathered} \text{Time taken by Fernando=Time taken by Davell} \\ (x)/(59)=(43-x)/(77) \\ 77x=(43*59)-59x \\ 77x+59x=2537 \\ 136x=2537 \\ x=(2537)/(136) \end{gathered}`

Solve for the time taken to meet as,

`\begin{gathered} T=(x)/(59) \\ T=(1)/(59)*(2537)/(136) \\ T\approx0.316 \end{gathered}`

Thus, it took approximately 0.316 hours for both of them to meet.