A bus covers a distance of 90km at a uniform speed. Had the speed been 15km/hour it would have taken 30 minutes less for the journey. Find the original speed of the bus.

Step-by-step explanation

Let's say d = distance, r = speed and t = time

We know the distance formula is :

distance = speed x time

d = r multiplied by t

d = rt

If the speed is 15km/hr, the time would be 30 minutes shorter.

Since d = rt,

90 = 15t

t = 6,

This means the time taken for the bus to complete the journey at 15km/hr would be 6hrs.

Originally though, the journey takes 30 minutes longer.

So we can say t = 6.5 hrs , and we know d = 90

Now we use the distance formula:

d = rt, since we want to find the original speed, we want to find r.

Speed = distance/time

r = d/t

r = 90/6.5

r = 180/13

Therefore the original speed is 180/13 km/hr