The interstate on-ramp is 1.5 km West of your home,and on leaving for grandmother's house you are only able to accomplish an average velocity of 12 km/hr between your home and the on-ramp.At the onramp,you wait for traffic,for 2.0 min - and then are able to proceed toward grandmother's house.If you wish to arrive there,which is 15 km South of the onramp,over a river and through some woods,in a total elapsed time of 25.0 minutes,what average speed must you maintain on the interstate highway?
A) 51 km/hr
B) 67 km/hr
C) 36 km/hr
D) none of these.

Question

Quizplus · Accepted Answer

First, let's convert the total elapsed time of 25.0 minutes to hours:

25.0 minutes = 25.0/60 hours = 0.417 hours

Now, let's find the total distance between the on-ramp and grandmother's house:

1.5 km (distance from home to on-ramp) + 15 km (distance from on-ramp to grandmother's house) = 16.5 km

We know that the time spent at the on-ramp waiting for traffic is 2.0 minutes, which is 2.0/60 hours = 0.033 hours.

So, the time spent driving on the interstate is:

0.417 hours (total elapsed time) - 0.033 hours (time spent at on-ramp) = 0.384 hours

Now we can use the formula:

average speed = total distance / total time

average speed = 16.5 km / 0.384 hours

average speed ≈ 43 km/hr

However, we need to remember that the average velocity from home to the on-ramp was only 12 km/hr. This means that for the first part of the trip, the average speed was lower than the overall average speed. So, to maintain an overall average speed of 43 km/hr, we need to travel faster than 43 km/hr on the interstate.

Let's call the speed we need to maintain on the interstate "x". We can set up the following equation:

(1.5 km / 12 km/hr) + (15 km / x) = 0.384 hours

Solving for x:

1.5/12 + 15/x = 0.384

15/x = 0.384 - 1.5/12

15/x = 0.32

x = 15/0.32 ≈ 47 km/hr

Therefore, we need to maintain an average speed of approximately 47 km/hr on the interstate in order to arrive at grandmother's house in a total elapsed time of 25.0 minutes.

The closest answer choice is B) 67 km/hr, which is not exactly correct, but is the best choice given the options provided.

The Interstate On-Ramp Is 1