Question

A farmer travelled a distance of 61 km on foot at an average speed of 4km/hr and partly on bicycle at an average speed of 9km/hr and the total distance is travelled in 9 hours. Then find the distance travelled by him on foot?
A. 14 km
B. 15 km
C. 16 km
D. 17 km

Answer 1

Hint: Speed is the ratio of distance travelled and time taken. Total distance is 61km, which is divided into distance travelled by bicycle and distance travelled on foot. Let the distance travelled on foot be x km, then the distance travelled by bicycle will be (61-x) km. Find the time taken to travel x km and (66-x) km, add the times and equate it to 9 hours to find the distance travelled by the farmer on foot.

Complete step-by-step answer:
We are given that a farmer travelled a distance of 61 km on foot at an average speed of 4km/hr and partly on bicycle at an average speed of 9km/hr in 9 hours.
We have to find the distance travelled by him on foot.
Let the distance travelled by the farmer on foot be x km.
Then the distance travelled by the farmer by bicycle will be $\left(61-x\right)km$
Speed is distance divided by time, time is distance divided by speed.
Using this, find the time taken by the farmer on foot and on bicycle.
 $$\begin{gathered} Tim{e}_{foot}={\displaystyle \frac{dis{t}_{foot}}{spee{d}_{foot}}} \\ spee{d}_{foot}=4km/hr,dis{t}_{foot}=xkm \\ \Rightarrow Tim{e}_{foot}={\displaystyle \frac{x}{4}}hours \\ Tim{e}_{bicycle}={\displaystyle \frac{dis{t}_{bicycle}}{spee{d}_{bicycle}}} \\ dis{t}_{bicycle}=\left(61-x\right)km,spee{d}_{bicycle}=9km/hr \\ \Rightarrow Tim{e}_{bicycle}={\displaystyle \frac{\left(61-x\right)}{9}}hours \end{gathered}$$
Total time is equal to time taken by the farmer on foot and on bicycle.
 $$\begin{gathered} Tim{e}_{total}=Tim{e}_{foot}+Tim{e}_{bicycle} \\ Tim{e}_{total}=9hours \\ \Rightarrow 9={\displaystyle \frac{x}{4}}+{\displaystyle \frac{61-x}{9}} \\ \Rightarrow 9\times 36=9x+4\left(61-x\right) \\ \Rightarrow 324=9x+244-4x \\ \Rightarrow 5x+244=324 \\ \Rightarrow 5x=324-244 \\ \Rightarrow 5x=80 \\ \Rightarrow x={\displaystyle \frac{80}{5}} \\ \therefore x=16km \end{gathered}$$
Therefore, the distance travelled by the farmer on foot is 16 km.

So, the correct answer is “Option C”.

Note: One kilometre is equal to 1000 metres; one hour is equal to 60 minutes and one minute is equal to 60 seconds. Use this information to convert kilometres into metres, hours into minutes, minutes into seconds and vice-versa. Here there was no need for any conversion because all the units are in km and hours. When one unit of length is in x and another unit of length is in y, then convert the both lengths into either x or y for an easy approach.