Question

A cyclist travels 8 km in the same time that a walker travels 3 km. The speed of the cyclist is 8 km/h more than the speed of the walker. Find the speed of the cyclist and the speed of the walker.

Answer 1

speed of cyclist = 12.8 km/h

speed of walker = 4.8km/h

The distance the cyclist traveled = 8km

A walker traveled = 3km

Let the speed of the work be x

The speed of the cyclist is 8 km/h more than the speed of the walker

Speed of the cyclist = (x + 8) km/h

Speed = distance / time

Cross multiply

Distance = speed x time

time = distance / speed

For the cyclist

Time = 8 / (x + 8) ---------- equation 1

For walker

time = 3 / x

Since, they both traveled at the same time

Equate the two equations together

`\begin{gathered} \frac{8}{(x\text{ + 8)}}\text{ = }(3)/(x) \\ \text{Cross multiply} \\ 8\cdot\text{ x = 3(x + 8)} \end{gathered}`

8x = 3x + 24

Collect the like terms

8x - 3x = 24

5x = 24

Divide both sides by 5

5x/5 = 24/5

x = 4.8 km/h

The speed of the walker is 4.8 km/h

Speed of the cyclist = x + 8

Since x = 4.8

Speed of the cyclist = 4.8 + 8

Speed of the cyclist = 12.8 km/h