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Liz drove from point A to point B at 40km/h. On her way back

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by AAPL » Sat Feb 24, 2018 5:18 am
Liz drove from point A to point B at 40km/h. On her way back she drove at 50km/h and therefore her way back lasted one hour less. what is the distance (in kilometers) between A and B?

A. 150.
B. 200.
C. 450.
D. 500.
E. 600.

The OA is B.

Can I say that

Distance from A to B = Speed * time = 40t

Distance from B to A = Speed * time = 50(t-1)

Then, 40t = 50(t-1) => t = 5, therefore Distance from A to B is 40*5 = 200 kilometers.

Is there a strategic approach to this question? Can any experts help? Thanks!
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by Brent@GMATPrepNow » Sat Feb 24, 2018 7:06 am
AAPL wrote:Liz drove from point A to point B at 40km/h. On her way back she drove at 50km/h and therefore her way back lasted one hour less. what is the distance (in kilometers) between A and B?

A. 150.
B. 200.
C. 450.
D. 500.
E. 600.
Let's start with a word equation

travel time at 40 kmh = travel time at 50 kmh + 1 hour
time = distances/speed
Let d = the distance from A to B

So, we get: d/40 = d/50 + 1
Multiply both sides by 200 to get: 5d = 4d + 200
Solve: d = 200

Answer: B

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Brent
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by Brent@GMATPrepNow » Sat Feb 24, 2018 7:06 am
AAPL wrote:Liz drove from point A to point B at 40km/h. On her way back she drove at 50km/h and therefore her way back lasted one hour less. what is the distance (in kilometers) between A and B?

A. 150.
B. 200.
C. 450.
D. 500.
E. 600.

The OA is B.

Can I say that

Distance from A to B = Speed * time = 40t

Distance from B to A = Speed * time = 50(t-1)

Then, 40t = 50(t-1) => t = 5, therefore Distance from A to B is 40*5 = 200 kilometers.

Is there a strategic approach to this question? Can any experts help? Thanks!
Hi AAPL,

Your solution is perfect.

Cheers,
Brent
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by GMATGuruNY » Sun Feb 25, 2018 4:17 am
AAPL wrote:Liz drove from point A to point B at 40km/h. On her way back she drove at 50km/h and therefore her way back lasted one hour less. what is the distance (in kilometers) between A and B?

A. 150.
B. 200.
C. 450.
D. 500.
E. 600
An alternate approach is to PLUG IN THE ANSWERS, which represent the distance.
Since the time difference yielded by the two speeds is an INTEGER VALUE -- one hour -- the correct answer is almost certain to be a multiple of the two speeds.
Of the five answer choices, only B, D and E are divisible by both 40 and 50.
When the correct answer is plugged in, the two speeds will yield a time difference of one hour.

B: 200
At a speed of 40mph, the time to travel 200 miles = d/r = 200/40 = 5 hours.
At a speed of 50mph, the time to travel 200 miles = d/r = 200/50 = 4 hours.
Time difference = 5-4 = 1 hour.
Success!

The correct answer is B.
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TTT

by deloitte247 » Sat Mar 03, 2018 12:47 pm
If the time taken at 40km/h is x, distance, d=40km/h * xhours= 40x km
At 50km/h
d=50 km/h * (x-1)h = 50(x-1) km
40x= 50(x-1) = 50x- 50
10x=50
x=5 and d= 40 (5)= 200km

Therefore the correct option is b
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