1.

With an average speed of 40 km/h, a motorcyclist reaches his destination in time. If after traveling 30 kms the motorcycle undergoes a problem and the average speed of motorcycle reduces to 30 km/h for the remaining journey. He is late by 20 minutes then it would have taken if the problem had not occurred. The length of the total journey is:1). 40 km2). 70 km3). 30 km4). 80 km

Answer»

LET the time taken by motorcyclist when travelling at 40 kmph be ‘t’ hours.

∴ Total distance travelled = (40 × t) km-----(1)

Now, after 30kms the motorcycle undergoes a problem and its speed reduces and it reaches the destination 20 mins late, that is, 1/3 hours late.

In this case, total time REQUIRED for journey = t + 1/3 hours

But time required to TRAVEL first 30kms = 30/40 = ¾ hours

∴ Time for which it travelled at 30 km/hr = t + 1/3 – ¾ = t – 5/12

∴ Total distance travelled = 30 + 30(t – 5/12) = 17.5 + 30t----(2)

From (1) and (2),

40t = 17.5 + 30t

10T = 17.5

t = 1.75 hours

∴ Total distance = 40 × 1.75 = 70 km


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