Question

The distance between two stations is 300 km. Two motor-cyclists 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 motor-cyclist. Check your solution.

Answer 1

Hint: To solve the above problem we will prepare a diagram to get the clear idea about the given situation in the question and then we will take the velocity of the one motor-cyclist as $v$ and velocity of the other motor-cyclists as $(v + 7)$.

Complete answer:

Given,
Distance between the two stations, $d = 300Km$
The speed of one of the motor-cyclists is $7$ km/h more than that of the other.
Time of journey, $t = 2$hours
The distance between the two motor-cyclist after 2 hours = ${d_x} = 34$Km
Now we will assign the velocities to the two motor-cyclists.
Let us suppose that the speed of the one of the motor-cyclist A = $v$km/h
Since it is given that the speed of one of the motor-cyclists is $7$ km/h more than that of the other.
So, the speed of the one of the other motor-cyclist B = $(v + 7)$km/h
After 2 hours,
$300 = (v \times 2) + \left[ {(v + 7) \times 2} \right] + 34$--------equation (1)
(using the formula,\[distance = speed \times time\], then equating the total distance to the sum of all the distances covered by the two motor-cyclist and the distance between them)
$ \Rightarrow 300 = 2v + 2v + 14 + 34$
$ \Rightarrow 300 = 4v + 48$
$ \Rightarrow 300 - 48 = 4v$
$ \Rightarrow 4v = 300 - 48$
$ \Rightarrow 4v = 252$
$ \Rightarrow v = \dfrac{{252}}{4}$
$ \Rightarrow v = 63$m/s
So the velocity of one of the motor-cyclists is $63$m/s and then the velocity of the other motor-cyclist is $(v + 7) = (63 + 7) = 70$m/s.
Checking the answer-
In the equation (1),
\[LHS = {\text{ }}300{\text{ }}Km\]
Now, Putting the value of the $v$ in the RHS of the equation (1), we get
$RHS = (63 \times 2) + \left[ {\left( {63 + 7} \right) \times 2} \right] + 34$
$ \Rightarrow RHS = 126 + \left[ {70 \times 2} \right] + 34$
$ \Rightarrow RHS = 160 + 140$
$ \Rightarrow RHS = 300$
Hence $LHS = RHS$
So, the answer is correct.

Note:
Speed of any of the body which is travelling some distance is the rate of change of position of the particular body. That means speed is equal to the distance divided by the time. The unit of the speed can be Km/h or m/s. There is a shortcut to convert the Km/h into m/s and m/s into Km/h. To change the unit from Km/h to m/s we should multiply the value of the speed by \[\dfrac{5}{{18}}\], while to change the m/s into Km/h we will multiply the value of the speed by $\dfrac{{18}}{5}$.