Question

The distance between the 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 $\dfrac{\text{km}}{\text{hr}}$ faster than the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist.

Answer 1

Hint: In this question use the given information to make the equations and remember to take the speed of first motorcyclists as x and speed of second motor-cyclist will be (x + 7) $\dfrac{\text{km}}{\text{hr}}$, use this information to approach towards the solution.

Complete step-by-step solution -
According to the given information, we know that the distance between two stations is 300 km when 2 motorcyclists started moving towards each other after 2 hours the distance between them becomes 34 km when one of the motorcyclist speed was $7 \dfrac{\text{km}}{\text{hr}}$ faster than the other
So let speed of 1 motorcyclist be $x \dfrac{\text{km}}{\text{hr}}$
Thus the speed of another motorcyclist will be $(x + 7) \dfrac{\text{km}}{\text{hr}}$
Let A and B be the two stations of motorcyclist
Let y be the distance traveled by the 1 motorcyclist
So by the formula of distance i.e. distance = $\text{speed} \times \text{time}$
So distance travelled by 1 motorcyclist $y = x \times 2$
$Y = 2x$
Let z be the distance traveled by the second object
So the distance travelled by the second motorcyclist after 2 hours will be $z = (x + 7)\times 2$
$4z = 2x + 14$
As we know that the total distance between 2 stations is 300 $\text{km}$
Therefore total distance = distance travelled by first motorcyclist after 2 hr + distance travelled by the second motorcyclist after 2 hr + distance remaining between both motorcyclist after 2 hrs so the equation formed will be $2x + 2x + 14 + 34 = 300$
$ \Rightarrow 4x = 300 – 48$
$ \Rightarrow x = \dfrac{{252}}{4}$
$ \Rightarrow x = 63$
So the speed of the first motorcyclist is $63 \dfrac{\text{km}}{\text{hr}}$ and the speed of the second motorcyclist is $(63 + 7) = 70 \dfrac{\text{km}}{\text{hr}}$.

Note: In the above solution we found the speed of motorcyclists by using the basic concept that after the 2 hours the sum of distance traveled by motorcyclists and distance between motorcyclists after 2 hours will be equal to the total distance, so know the only thing we want that the distance traveled by the motorcyclists after 2 hours so we used the formula distance i.e. distance = speed \[ \times \] time. Speed is represented by x km/hr so here it means that an object travels x km in 1 hr.