Question

Points A and B are 90 km apart on a highway. A car starts from A and another from B at the same time. If they travel in the same direction they meet in 9 hours and if they travel in opposite directions they meet in $\frac{9}{7}$ hours. Speed of car starting from point A is:

• A. 30 km/hr
• B. 90 km/hr
• C. 40 km/hr
• D. 220 km/hr

Answer 1

The correct option is C

40 km/hr

Let X and Y be two cars starting from points A and B respectively. Let the speed of car X be x km/hr and that of car Y be y km/hr.
Case I: When the two cars move in the same direction:
Suppose two cars meet at point Q.
Distance travelled by car X = AQ
Distance travelled by car Y = BQ
$\therefore$ Distance travelled by car X in 9 hours = 9x km $\Rightarrow$ AQ = 9x
Distance travelled by car Y in 9 hours = 9y km $\Rightarrow$ BQ = 9y

Clearly, AQ - BQ = AB [$\because$ AB = 90 km]
$\Rightarrow$ 9x - 9y = 90 $\Rightarrow$ x - y = 10 . . . . (1)

Case II: When two cars move in opposite direction:
Suppose two cars meet at point P.
Distance travelled by car X = AP.
Distance travelled by car Y = BP.
In this case, two cars meet in $\frac{9}{7}$ hours.

Distance travelled by car X in $\frac{9}{7}hours=\frac{9}{7}xkm\Rightarrow AP=\frac{9}{7}x$

Distance travelled by car Y in $\frac{9}{7}hours=\frac{9}{7}ykm\Rightarrow BP=\frac{9}{7}y$
Clearly, AP + BP = AB

$\Rightarrow \frac{9}{7}x+\frac{9}{7}y=90\Rightarrow \frac{9}{7}(x+y)=90$

$\Rightarrow$ x + y = 70 . . . . (2)
Adding equations (1) and (2),
x - y = 10 ....(1)
x + y = 70 .....(2)
________
$\Rightarrow$ 2x = 80
$\Rightarrow$ x = 40
Substitute x = 40 in eq. (1)
40 - y = 10
y = 40 - 10 = 30
$\therefore$ x = 40 and y = 30
Hence, speed of car starting from point A is 40 km/hr.