Problem Solving

Q. If Deepti had walked 20km/h faster, she would have saved 1 hour in the distance of 600 km. what is usual speed of Deepti?
a) 100
b)120
c)150
d)none of these

Distance/Rate = Time

Let her usual rate be R.

Translate the question into math.

600/R - 1 = 600/(R + 20)

Solve.

600R + 12,000 - R² - 20R = 600R

0 = R² + 20R - 12,000

Factor.

(R + 120)(R - 100) = 0

R = -120 or 100

Use only the positive rate.

The correct answer is a.

Alternative Method: Plug in the answer choices.

(a) 100

R = 100

R + 20 = 120

600/100 = 6

600/120 = 5

6 - 1 = 5

The correct answer is a.

Joy Shaha wrote:Q. If Deepti had walked 20km/h faster, she would have saved 1 hour in the distance of 600 km. what is usual speed of Deepti?
a) 100
b)120
c)150
d)none of these

We can PLUG IN THE ANSWERS, which represent the usual speed.
When the correct answer choice is plugged in, traveling 20kph faster will take 1 hour less than traveling at the usual speed.

The answers choices imply the following:
A: 100kph = usual speed, 120kph = faster speed
B: 120kph = usual speed, 140kph = faster speed
C: 150kph = usual speed, 170kph = faster speed

Since the difference between the two times is an integer value, the two speeds are almost certain to divide evenly into the distance of 600k.
Only A offers two values that divide evenly into 600.

A: 100kph = usual speed, 120kph = faster speed
Time at the usual speed = d/r = 600/100 = 6 hours.
Time at the faster speed = d/r = 600/120 = 5 hours.
Time difference = 6-5 = 1 hour.
Success!

The correct answer is A.

Joy Shaha wrote:Q. If Deepti had walked 20km/h faster, she would have saved 1 hour in the distance of 600 km. what is usual speed of Deepti?
a) 100
b)120
c)150
d)none of these

Assume current speed = x
Total time taken for 600 km = 600/x

Total time taken at x + 20 speed = 600/(x + 20)

Given,
600/x - 600/(x + 20) = 1
x^2 + 20x -12000 = 0
(x + 120)(x - 100) = 0
x = -120 or 100

Correct Option: A

ceilidh.erickson wrote:Just note that this is not a real GMAT-style problem. GMAT PS problems will always have 5 answers choices, not 4.

Four answers (especially if one of them is "none of these") on a GMAT forum post typically indicates a CAT question. These Qs seem fair game here, since that exam covers most of the same math topics as the GMAT (albeit with harder problems on the whole).