Question

The time t required to drive a certain distance varies inversely with the speed r. If it takes 2 hours to drive the distance at 30 miles per hour, how long will it take to drive the same distance at 50 miles per hour?. A.. . 60 hours. . B.. . 1.2 hours. . C.. . 750 hours. . D.. . about 3.33 hours

Answer 1

The time taken to travel a distance of 60 miles at the speed of 50 miles per hour is:

1.2 hours. ( Option: B)

Explanation:

It is given that:

The time t required to drive a certain distance varies inversely with the speed r.

Let d denotes the distance traveled.

We know that:

`Distance=speed* time`

i.e.
`d=rt`

Now it takes 2 hours to drive the distance at 30 miles per hour.

i.e. we have t=2 hours

r=30 miles per hour.

Hence, the distance traveled is:

`d=2* 30\\\\d=60\ miles.`

Now, we are asked to find the time taken to drive the same distance at 50 miles per hour i.e. we have d=60 miles.

and r=50 miles per hour.

Hence,

`60=t* 50\\\\t=(60)/(50)\\\\t=(6)/(5)\\\\t=1.2\ hours`

Hence, option: B is the correct answer.

B. 1.2 hours.

Answer 2

The inverse variation between time t and speed r is shown below,
t = k / r
where k is the constant of inverse variation which we know is the distance.
For the first set of given,
2 hours = k / 30 mph ; k = 60 miles
For the second set,
t = 60 miles / 50 mph ; t = 1.2 hours
Thus, the answer is letter B.