A car travels from point A to point B. The average speed of the car is 60 miles/hr and

BTGModeratorVI wrote: ↑

Sun Apr 05, 2020 8:58 am

A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

A. 30
B. 45
C. 60
D. 75
E. 90

Answer: B
Source: Grockit

Say the distance from Point A to Point B = 2d miles

Thus, the car took 2d/60 = d/30 hours to travel from Point A to Point B

As per the information, d miles were traveled with the speed of 60 mph.

Thus, the car took d/90 hours to travel first half the distance from Point A to Point B.

=> time taken to cover the second half = d/30 – d/90 = d/45 hours

Speed in the second half of the trip = d/(d/45) = 45 mph

The correct answer: B

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Sun Apr 05, 2020 8:58 am

A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

A. 30
B. 45
C. 60
D. 75
E. 90

Answer: B
Source: Grockit

There's a bit of ambiguity here.

If the first half of the trip is spent at one speed, and the second half is spent at another speed, are we referring to half the total DISTANCE, or half the total TIME.
For example, if it takes 10 hours to drive 200 miles, some people might refer to the first half of the trip as being the first 5 hours of driving. Others might refer to the first half of the trip as being the first 100 miles traveled.

That said, the official answer informs us that we're talking about half the DISTANCE.

To make things easier for us, let's assign a NICE VALUE to the TOTAL distance. That is, a number that works well with 60 and 90

Let's say the TOTAL distance is 540 miles.
This means the car traveled 270 miles at 90 mph, and the car traveled 270 miles at x mph.
It also means the car traveled the TOTAL 540 miles at an average speed of 60 mph

Let's start with a word equation: time spent driving 90 mph + time spent driving x mph = TOTAL time of trip
Time = distance/speed
So, we now get: 270/90 + 270/x = 540/60
Simplify to get: 3 + 270/x = 9
This means that 270/x = 6
Multiply both sides by x to get: 270 = 6x
Solve: x = 45 (mph)

Answer: B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sun Apr 05, 2020 8:58 am

A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

A. 30
B. 45
C. 60
D. 75
E. 90

Answer: B
Source: Grockit

We can use the formula:

average = total distance / total time

Let’s denote the total distance by d and the unknown speed of the car in the second half of the trip by r.

60 = d / [(d/2)/90 + (d/2)/r)]

60 = d / [d/180 + d/2r]

60[d/180 + d/2r] = d

d/3 + 30d/r = d

d(1/3 + 30/r) = d

1/3 + 30/r = 1

30/r = 2/3

2r = 90

r = 45

Answer: B