The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist.

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63km/h, 70km/h

70km/h, 77km/h

60km/h, 67km/h

None of these

answer is A.

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Detailed Solution

It is given that there are 2 motorcyclists with the speed of one of them is 7 km/h more than that of the other. The distance between two stations is 300 km.
The formula for the speed is given as follows,

Speed = Distance Time

.
Assume the speed of the first motorcyclist to be x km/h.
Then, the speed of the second motorcyclist will be (x+7) km/h.
So, according to the condition, both the motorcyclists travel for 2 hours.
So, we will find the distance covered by them in 2 hours as follows,
Distance covered by first motorcyclist

⇒ 2 × x = 2 x

km
Distance covered by second motorcyclist

⇒ 2 × (x + 7) = 2 x + 14

km
Now, as per the condition, after 2 hours, the distance between the two motorcyclists is 34 km while they were initially 300 km away from each other.
So, we can say that the total distance, i.e., 300 km is nothing but the combined distance traveled by them in two hours plus the distance remaining, i.e., 34 km.
So, we can set up the equation as follows,