K6atn3bunnyHoldah
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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

Respuesta :

meerkat18
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. 

Answer:

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

1.2 hours.  ( Option: B)

Step-by-step 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:

[tex]Distance=speed\times time[/tex]

i.e. [tex]d=rt[/tex]

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:

[tex]d=2\times 30\\\\d=60\ miles.[/tex]

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,

[tex]60=t\times 50\\\\t=\dfrac{60}{50}\\\\t=\dfrac{6}{5}\\\\t=1.2\ hours[/tex]

Hence, option: B is the correct answer.

B.   1.2 hours.