The distance between two stations is 300 km. Two motor cyclists start simultaneously fr stations and move towards each other. The speed of one of them is 7 km/hr faster than ether. If the distance between them after 2 hours of their start is 34 km, find the apent motor-cyclist
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Answer:
Solution
The distance between two stations = 300 km
Let the speed of first motorcyclists = x km/h
and speed of second motorcyclists = (x + 7) km/h
Distance covered by the first = 2x km
and distance covered by the second = 2 (x + 7) km = 2x + 14 km
∴
Distance uncovered by them = 300 - (2x + 2x + 14) kms.
According to the condition,
300 - (4x + 14) = 34
⇒
300 - 4x - 14 = 34
⇒
300 - 14 - 34 = 4x
⇒
4x = 300 - 48
⇒
4x = 252
⇒
x
=
252
4
=
63
∴
Speed of the first motorcyclists = 63 km/h
and speed of second = 63 + 7 = 70 km/h
Check. Distance covered by both of them
= 2
×
63 + 2
×
70 = 126 + 140 = 266
Total distance = 300 km.
∴
Distance between them = 300 - 266 = 34 km.
which is given
Step-by-step explanation:
The distance between two stations = 300 km
Let the speed of first motorcyclists = x km/h
and speed of second motorcyclists = (x + 7) km/h
Distance covered by the first = 2x km
and distance covered by the second = 2 (x + 7) km = 2x + 14 km
∴
Distance uncovered by them = 300 - (2x + 2x + 14) kms.
According to the condition,
300 - (4x + 14) = 34
300 - 4x - 14 = 34
300 - 14 - 34 = 4x
4x = 300 - 4x
4x = 252
252
4
=
63
∴
Speed of the first motorcyclists = 63 km/h
and speed of second = 63 + 7 = 70 km/h
Check. Distance covered by both of them
= 2
×
63 + 2
×
70 = 126 + 140 = 266
Total distance = 300 km.
∴
Distance between them = 300 - 266 = 34 km.