Question

Places A and B are 100km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 10 hours and if they move in opposite directions, they meet in 1 hour 40 minutes. Find the speed of the cars from places A and B respectively.

Answer 1

Hint – Here we will proceed by assuming the speed of both the cars from both the places A and B. Then by using the given distance we will form two equations i.e. when the car travels in the same direction and when the car travels in the opposite direction. Further we will solve the equations to get the speed of both the cars from the places A and B respectively.

Complete step-by-step answer:
Let the speed of the first car which starts from A = x km per hour
And speed of the second car which starts from B = y km per hour
Also given that the distance between both the places i.e. AB is 100km.
When the car travels in same direction-
Relative speed= (x – y) km per hour
As we know, $time={\displaystyle \frac{distance}{speed}}$
Now we will put the values of distance and time into the above mentioned formula to form the equation,
$\Rightarrow {\displaystyle \frac{100}{x-y}}=10$
$\Rightarrow$ 100 = 10(x – y)
$\Rightarrow x-y=10$………………… (1)
When the car travels in opposite direction-
Relative speed = (x + y) km per hour
As we know, $time={\displaystyle \frac{distance}{speed}}$
Now we will put the values of distance and time into the above mentioned formula to form the equation,
$\Rightarrow {\displaystyle \frac{100}{x+y}}=1{\displaystyle \frac{2}{3}}={\displaystyle \frac{5}{3}}$ [$\because$ 40 min = ${\displaystyle \frac{2}{3}}$ hour]
$\Rightarrow 300=5(x+y)$
$\Rightarrow x+y=60$ ………………. (2)
We will solve these two equations using substitution method,
Taking equation 1 i.e. x – y = 10, we will make another equation-
x = 10 + y ……… (3)
Now we will substitute the equation 3 i.e. x = 10 + y in equation 2,
$\Rightarrow 10+y+y=60$
$\Rightarrow 10+2y=60$
$\Rightarrow 2y=50$
$\Rightarrow y=25$
As we get the value of y, we will substitute the value of y in equation 1 i.e. x – y = 10,
$\Rightarrow x-25=10$
$\Rightarrow$ x = 35
Now we get,
$\therefore$ Speed of the car starts from place A = 35 km per hour.
Speed of the car starts from place B = 25 km per hour.

Note – We can also use elimination method, augmented matrices instead of substitution method to solve the equations. Also one can get confused while calculating the relative speed of both the cars, so we must concentrate while forming the equations.