Question

The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist. Check your solution.

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=2524=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. MathematicsSecondary School Mathematics VIIIStandard VIII

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