Can someone give me confirmation?

Question

A driver travels without stopping for 3 hours on the interstate at speeds ranging from 60 miles per hour to 70 miles per hour. What is the approximate minimum additional time required to drive a distance of 300 miles away from the starting point if the driver maintains the same range of speeds?

NOTE: I chose "A" if I'm wrong, how so?

A. 1.5 hrs.

B. 2 hrs.

C. 2.5 hrs.

D. 3 hrs.

Answer 1

You may determine the possible range of distances already travelled in the three hours, but since the problem asks for the "approximate minimum additional time," then using the maximum of that range provides the minimum additional time.  So, at 70 miles/hr, the maximum possible distance travelled so far is (70*3 miles).  That leaves 90 miles (note: 300-210) remaining to travel. 

In order to travel 90 miles in the "minimum additional time," the maximum possible speed is used in the calculation.  It will take at least (90/70 hours), nearly 1.5 hours, to complete the trip.  So, 1.5 hours is a good estimate of the minimum.

 

Now, since the choices are quite rough, you could very quickly estimate the answer using the fact that 60 mph means travelling 60 miles per hour and a 300 mile trip would take 5 hours.  Three hours have already been spent, leaving 2 hours.  This is the slowest speed and the longest time for this trip ("same range of speeds" and "without stopping").  Since the driver may travel up to 10 mph faster than this, the minimum is lower than 2 additional hours.

Answer 2

Hello Bran

 

If the driver speed is between 60 and 70mph, that means he has driven between 180 and 210 miles, as a result of multiply 3 hours and both speeds.

 

In other words, he needs to drive between 90 and 120 miles to complete 300 miles. So the minimum additional time he should spend is what it takes to drive 90 miles at the lower speed. 90 miles at 60 mph.

 

Therefore, you are right. 90/60=1.5 hours

 

Of course you can say, if he drove at 60mph the first 3 hours the answer is 2 hours because 120/60 is 2. However, in that case we have to think that he drove in an average speed between 70 and 60 mph. That means he drove at 65mph. In that case he drove 195 miles and the rest is 105 to 300 miles. 105/60 is 1.62 hours which is closer to 1.5 the first answer.

 

 

I hope it had helped you.

 

 

Fernando

Answer 3

Figure out how many miles you go in the first 3 hours:

3 hours * 60miles/1hour =180miles (hours cancel out leaves you with just miles)

 

Figure out how many miles you have left to go to go a total of 300 miles:

300miles-180miles= 120 miles

 

Set up the problem (how many miles you go = how many hours you drive * speed):

120miles=xhours *60miles/hour

 

Solve  for x:

1hour/60miles * 120 miles =xhours (multiply by the reciprocal of 60miles/hour)

 

Solve:

2 hours = x hours (miles cancels out your answer is in hours)

 

The answer is B:2hrs