Question

A tour bus normally leaves for its destination at 5:00 p.m. for a 300 mile trip. This week however, the bus leaves at 6:00 p.m. To arrive on time, the driver drives 10 miles per hour faster than usual. What is the bus` usual speed?

The bus' usual speed is ---- miles an hour.

Answer 1

Let x be the usual speed and it takes t hours to reach 300 mile destination

t=300/x

And Latter it's speed is x+10 miles/hour and it takes t-1 hours to complete 300 mile trip

We know that, distance=speed * time

The distance travelled in both cases is same which is 300 miles

Therefore x*t=(x+10)( t-1)

Xt=xt-x+10t-10

Therefore x=10(t-1) since t=300/x

x=10((300/x)-1)

X²=3000-10x

X²+10x-3000=0

X²+60x-50x-3000=0

X(x+60)-50(x+60)=0

(X-50)(x+60)=0

Therefore x=50,-60

The usual speed is 50 miles/hour