Points A and B are 70 km apart on a high way. A car starts from A and anothercar starts from B at the same time. If they travel in the samedirection, they meet in 7 hours, but if they travel towards eachother they meet in one hour, what are their speeds?.
Let the speed of the car starting from A be at x km/hr and that starting from B be at y km/hr.
Condition 1:
If the cars travel in the same direction, they meet in 7 hrs.
We know that,
Distance = Speed x Time
. . . Distance covered by car starting from A in 7 hours = 7x km.
and distance covered by car starting from B in 7 hours = 7y km
. . . 7x - 7y = 70
i.e. x - y = 10 (dividing by 7 throughout ) ⌠(i)
Condition 2:
If the cars travel in opposite direction, they meet in 1 hour.
. . . Distance covered by car starting from A in 1 hour = x km.
and distance covered by car starting from B in 1 hour = y km.
. . . x + y = 70 ⌠(ii)
from (i) and (ii)
x - y = 10
x + y = 70
__________
2x = 80
x = 80/2
x = 40 km/hr
Substitute x = 40 in (ii)
40 + y = 70
y = 70 - 40
y = 30 km/hr.
. . . The speed of the car starting from A is 40 km/hr.
and the speed of the car starting from B is 30 km/hr.
Verification:
(a) x - y = 40 - 30 = 10
(b) x + y = 40 + 30 = 70.
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