Question

I started on my bicycle at 7 A.M. to reach a certain place. After going a certain distance, my bicycle went out of order. Consequently, I rested for 35 minutes and came back to my house walking all the way. I reached my house at 1 P.M. If my cycling speed is 10km/hr and my walking speed is 1 km/hr, then what distance did I cover on my bicycle?
A. \[3\dfrac{{61}}{{66}}km\]
B. \[4\dfrac{{61}}{{66}}km\]
C. \[6\dfrac{{61}}{{66}}km\]
D. \[7\dfrac{{61}}{{66}}km\]

Answer 1

Hint: For solving this question, we will consider \[T\] be the time taken till the bicycle went out of order, and then we can calculate distance travelled. And with this we will proceed further accordingly. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
Let us consider that \[T\] be the time taken till the bicycle went out of order.
Given that his cycling speed is 10km/hr.
We know that \[{\text{distance}} = {\text{speed}} \times {\text{time}}\].
Then distance travelled when bicycle went out of order \[ = 10 \times T\]
The person went out at 7 A.M and returned home at 1 P.M. So, the total time taken by him to come back to home = 6 hours.
Also, given that the person has rested for a time of 35 minutes i.e., \[\dfrac{{35}}{{60}}\] hours.
Now, time taken for walking = total time taken to return – time taken by cycling – time taken for rest
  \[ = 6 - \dfrac{{35}}{{60}} - T\]
Given that the person walked with a speed of 1 km/hr.
We know that \[{\text{distance}} = {\text{speed}} \times {\text{time}}\].
So, the distance travelled by the person by walk \[ = 1 \times \left( {6 - \dfrac{{35}}{{60}} - T} \right) = 6 - \dfrac{{35}}{{60}} - T\]
Now, according to the question, distance travelled by cycling and distance travelled by walk are the same. So, we have
\[
   \Rightarrow 10T = 6 - \dfrac{{35}}{{60}} - T \\
   \Rightarrow 10T + T = \dfrac{{6 \times 60 - 35}}{{60}} \\
   \Rightarrow 11T = \dfrac{{360 - 35}}{{60}} \\
   \Rightarrow 11T \times 60 = 360 - 35 \\
   \Rightarrow 660T = 325 \\
  \therefore T = \dfrac{{325}}{{660}} \\
\]
We have to calculate the distance travelled by the bicycle i.e., \[10T = 10 \times \dfrac{{325}}{{660}} = \dfrac{{66 \times 4 + 61}}{{66}} = 4\dfrac{{61}}{{66}}km\].
Thus, the correct option is B. \[4\dfrac{{61}}{{66}}km\]


Note: We know the relation between speed, time and distance as: \[{\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}\]. Using this, we can calculate the distance travelled on a bicycle and the distance covered by walking. As the distance is the same according to the question, we can equate and solve for \[T\], And then we will put the value of \[T\], to get the distance covered on a bicycle. The distance covered by the bicycle and by walk are equal. Only, the speed and time taken by them are different and are inversely proportional to each other.