Question

If Dr. Bob ride his bike to his office he averages 12 mph if he drives his car he averages 48 mph his time driving is 1/4 hour less than his time bicycling how far is his office

Answer 1

2.4 miles

Explanation:

From the question;

• When using the bike, speed is 12 mph
• When using the car, the speed is 48 mph
• He takes 1/4 hrs less when using the car than when he uses the bike.

We are going to assume the distance to the office is x miles

Therefore;

Time taken when using the bike;

Time = distance ÷ speed

= x/12 hours

Time taken when using the car;

Time = x/48 hours

But, time taken when using the car is 1/4 hours less.

Therefore;

1/12 hours - x/48 hours = 1/4 hr

That is;

`(x)/(12) + (x)/(48)= (1)/(4)`

We want to solve for x.

Multiplying by LCM, 48

We get,
`4x + x = 12`

5x = 12

x = 12/5

= 2.4 miles

Therefore, the office is 2.4 miles away.