Question

Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.

Answer 1

Let the speed of the two cars be “x” and “y”.

By the given first condition

`100/(x + y) = 1("Distance"/"Speed" = "time")`

x + y = 100 ........(1) ......(They travel in opposite direction)

By the given second condition.

`100/(x - y)` = 2  ...[time taken in 2 hours in the same direction]

2x – 2y = 100

x – y = 50 ..........(2)

x + y = 100

y = 100 – x

x	30	50	60	70
y	70	50	40	30

Plot the points (30, 70), (50, 50), (60, 40) and (70, 30) in the graph sheet

x – y = 50

– y = – x + 50

y = x – 50

x	40	50	60	70
y	– 10	0	10	20

Plot the points (40, – 10), (50, 0), (60, 10) and (70, 20) in the same graph sheet

The two cars intersect at (75, 25)

The speed of the first car 75 km/hr

The speed of the second car 25 km/hr