Question

Drive to work in 45 min., bus to work takes 1 hr 15 min. If the average rate on the bus is 16 mph slower than his driving rate, how far does he travel to work?

Answer 1

Answer:

30 miles

Step-by-step explanation:

Given: Drive to work in 45 min.

           Bus would take to travel= 1 hr 15 min

          Average rate on the bus is 16 mph slower than his driving rate.

Lets assume the average driving rate be "x" mph.

∴ Average rate of bus= $(x-16)\ mph$

Now converting unit of time taken to travel to work.

Remember; 1 hours= 60 minutes.

Time taken for drive to work= $\frac{45\ minutes}{60\ minutes} = 0.75\ hour$

Time taken in bus to work= 1 hour and 15 minutes=$60\ minutes+ 15\ minutes= 75\ minutes$

∴ Time taken in bus to work in hours= $\frac{75\ minutes}{60\ minutes}= 1.25\ hours$

Considering the distance remain constant to travel for work.

Next, forming an equation to find the value of x.

As we know, $distance= speed\times time$

⇒ $x\times 0.75= (x-16)\times 1.25$

Using distributive property of multiplication.

⇒$0.75x= 1.25x-20$

Adding both side by 20

⇒ $0.75x+20= 1.25x$

Subtracting both side by 0.75x

⇒$20= 0.5x$

Dividing both side by 0.5

⇒$x= \frac{20}{0.5}$

∴ $x= 40\ mph$

Hence the average rate for drive to work is 40mph.

Now, subtitiuting the value of x to find the distance travelled to work.

Distance travelled= $40\times 0.75= 30\ miles$

Hence, distance travelled to work is 30 miles.