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# A car drove from Town A to Town B without stopping. The car traveled

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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14 Sep 2015, 05:07
3
4
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:20) correct 27% (02:51) wrong based on 312 sessions

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A car drove from Town A to Town B without stopping. The car traveled the first 40 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 120 miles if the car’s average speed for the entire trip was 40 miles per hour?

(A) 28
(B) 48
(C) 50
(D) 55
(E) 70

Kudos for a correct solution.

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Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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14 Sep 2015, 06:11
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Bunuel wrote:
A car drove from Town A to Town B without stopping. The car traveled the first 40 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 120 miles if the car’s average speed for the entire trip was 40 miles per hour?

(A) 28
(B) 48
(C) 50
(D) 55
(E) 70

Kudos for a correct solution.

CONCEPT: Average Speed = Total Distance / Total Time

Total Distance of the trip = 40+120 = 160 miles
Average Speed over entire trip = 40 miles per hour
Total Time taken of entire trip = 160/40 = 4 hours

Time taken to cover first 40 miles of trip = 40/25 = 1.6 hour

Time Taken to cover Next 120 miles of trip = 120/x

Total Time of the trip = 4 = 1.6 + 120/x
i.e. 120/x = 2.4
i.e. x = 120/2.4 = 50 Miles per hour

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Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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14 Sep 2015, 11:12
For the 1st stage:
distance = 40 miles, speed = 25 mph → time t1 =40/25 = 8/5 hr

For the 2nd stage:
distance = 120 miles, speed = s, → time t2 = 120/s

For the total stretch;
Total Distance = 40+120 = 160 miles, Average speed = 40 mph, Total Time = Total Distance/ Average Speed = 160/40 = 4hr

Also Total Time = t1+t2 = 8/5+ 120/s = 4;
Solving for s → s = 50 mph.
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Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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18 Sep 2015, 05:16
1
Bunuel wrote:
A car drove from Town A to Town B without stopping. The car traveled the first 40 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 120 miles if the car’s average speed for the entire trip was 40 miles per hour?

(A) 28
(B) 48
(C) 50
(D) 55
(E) 70

Kudos for a correct solution.

Let average speed to cover 120 miles be x.

total time = time for 1st route + time for 2nd route
160/40= 40/25+120/x
Solving this eqn, x = 50(ans)
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Posts: 159
Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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18 Sep 2015, 05:57
2
Bunuel wrote:
A car drove from Town A to Town B without stopping. The car traveled the first 40 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 120 miles if the car’s average speed for the entire trip was 40 miles per hour?

(A) 28
(B) 48
(C) 50
(D) 55
(E) 70

Kudos for a correct solution.

Let x be the average speed for remaining 120 miles.
Total distance = 120 + 40 = 160
Total time = 40/25 + 120/x

Avg speed= Total distance / Total time

$$40$$=$$\frac{160}{\frac{40}{25} + \frac{120}{x}}$$

or $${\frac{40}{25} + \frac{120}{x} = 4$$

or $$\frac{8x+600}{5x}$$ = $$4$$

or $$20x = 8x+600$$

or $$12x = 600$$

or $$x= 50$$

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Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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18 Sep 2015, 21:57
1
Bunuel wrote:
A car drove from Town A to Town B without stopping. The car traveled the first 40 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 120 miles if the car’s average speed for the entire trip was 40 miles per hour?

(A) 28
(B) 48
(C) 50
(D) 55
(E) 70

Kudos for a correct solution.

The Answer will be 50 miles per hour.
First part distance traveled = 40 miles
Avg. Speed = 25 mph
Time taken = 40/25 = 8/5 hrs -- (A)

Second part distance traveled = 120 miles
Avg. Speed (say) = x mph
Time taken = 120/x hrs -- (B)

Total Distance traveled = 40 + 120 = 160 miles
Avg. speed for the whole journey = 40 mph
Total time to be taken = 160/40= 4 hrs -- (C)

Therefore From A and B, we get C i.e.

4 = 8/5 + 120/x
=> x = 50 mph

O.A. = C
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Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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19 Sep 2015, 01:34
Bunuel wrote:
A car drove from Town A to Town B without stopping. The car traveled the first 40 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 120 miles if the car’s average speed for the entire trip was 40 miles per hour?

(A) 28
(B) 48
(C) 50
(D) 55
(E) 70

Ans: C

Solution: avg speed = total distance / total time take

we know total distance is 120+40
and time taken for first 40 miles is 40/25 and for the remaining distance letssay t
so avg speed for the whole distance 40 = 160/ (40/25 + t)

this will make avg speed =50
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Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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19 Sep 2015, 03:36

160/40=40/25+12/x

solving gives x=50
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Posts: 50009
Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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20 Sep 2015, 21:37
Bunuel wrote:
A car drove from Town A to Town B without stopping. The car traveled the first 40 miles of its journey at an average speed of 25 miles per hour. What was the car’s average speed, in miles per hour, for the remaining 120 miles if the car’s average speed for the entire trip was 40 miles per hour?

(A) 28
(B) 48
(C) 50
(D) 55
(E) 70

Kudos for a correct solution.

KAPLAN OFFICIAL SOLUTION:

To solve this problem, you must remember that average speed means total distance divided by total time over an entire journey. This should not be confused with the average of the speeds. The total distance in this problem is 160 miles, but we will need to express the total time in a more complex way.

For the first 40 miles, the car traveled at 25 miles per hour. Therefore, we can say that the time this took was 40/25, because distance divided by rate equals time.

For the last 120 miles, we are trying to solve for the rate, so we can call this speed R. Thus, the time for the final 120 miles is 120/R.

If we put all of this together, knowing that the average speed over the entire journey is 40 miles per hour, we get the equation 160/(40/25 + 120/R) = 40. We can now solve for R and reach our answer.

160/(40/25 + 120/R) = 40

4/(8/5 + 120/R) = 1

4 = 8/5 + 120/R

4R = 8R/5 + 120

20R = 8R + 600

5R = 2R + 150

3R = 150

R = 50

50 is choice (C) and that’s our correct answer.
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Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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02 Oct 2015, 01:46
40/25 + 120/x=4, got equation so can go backsolving

take x=50 (option C) 80/50+120/50=200/50=4

C
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Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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11 Jun 2017, 18:40
My approach:
distance = speed x time

40 = 25 t (time = 1 3/5)
120 = st
160 = 40 t (time = 4)

120 = st

1 3/5 + t = 4
t = 2 2/5

2 2/5 x speed = 120
12/5 s = 120
s = 120(5)/12
s = 50

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Re: A car drove from Town A to Town B without stopping. The car traveled  [#permalink]

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26 Jul 2018, 17:54
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Re: A car drove from Town A to Town B without stopping. The car traveled &nbs [#permalink] 26 Jul 2018, 17:54
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