A bus averages 2miles per hour faster than a motorcycle. If the bus travels 165miles in the same time it takes the motorcycle to travel 155miles, then what is the speed of each?

speed of bus = 33 mi/hr

speed of motorcycle = 31 mi/hr

Step-by-step explanation:

Let the speed of the motorcycle be x mi/h.

Now, we are told that the bus averages 2 mi/hr faster than the motorcycle. Thus, speed of bus = (x + 2) mi/hr

Formula for time is; t = distance/speed

Since distance covered by bus is 165 miles, then t_bus = 165/(x + 2)

Since distance covered by motorcycle is 155 miles, then t_motorcycle = 155/x

We are told that the bus and the motorcycle used the same time to cover their respective distances. Thus;. t_bus = t_motorcycle

Thus;

165/(x + 2) = 155/x

Cross multiply to get;

165x = 155(x + 2)

165x = 155x + 310

165x - 155x = 310

10x = 310

x = 310/10

x = 31 mi/hr

Then speed of bus = 31 + 2 = 33 mi/hr