Question: The distance between Bandel and Asansol is 100 Km. A leaves Bandel for Asansol and walks at the rate...

Question

The distance between Bandel and Asansol is 100 Km. A leaves Bandel for Asansol and walks at the rate of 3km/hr. 3 hrs later, B starts from Asansol for Bandel and walks at 3.5km/hr. Find the distance from Asansol where they would meet?
(a) 51km
(b) 49km
(c) 52km
(d) 53km

Answer 1

Solution

Hint: Let the time from the time when B starts from Asansol after which A and B meet be t hrs. We know $\text{distance=speed}\times \text{time}$ , so distance travelled by B is equal to 3.5t km and the distance travelled by A is 3(t+3) km, as A travelled 3 hrs more as compared to B. Now we will add up the distances and equate it to 100km, as the total distance covered by them is equal to distance between the starting points and solve the equation to get the value of t. Once you get t, find the distance covered by t to get the answer.

Complete step-by-step answer:
Let us start the solution by letting the time from the time when B starts from Asansol after which A and B meet be t hrs.
We know that $\text{distance=speed}\times \text{time}$ , so distance travelled by B is equal to 3.5t km and the distance travelled by A is 3(t+3) km, as it is given that B started 3 hrs after A, so A travelled 3 hours more.
Now if we add the distances travelled by A and B we must get the distance between their starting points, as they are at the same location when they meet and are moving in a straight line. So, if we form the equation and solve, we get
$3.5t+3\left( t+3 \right)=100$
$\Rightarrow 3.5t+3t+9=100$
$\Rightarrow 6.5t=91$
$\Rightarrow t=\dfrac{91}{6.5}=14hrs$
So, they will meet after 14 hrs after the time B has started from Asansol. Also, the distance from Asansol of their meet point will be equal to distance travelled by B, i.e., $3.5t=3.5\times 14=49km$ .
Therefore, the answer to the above question is option (b).

Note: Be very careful about the distance which is asked, whether it is from Asansol or the other place Bandel. Also, be very careful about the time t you are considering, whether it is from the starting time of B or from the starting time of A and proceed accordingly.