Stacy and Heather are 20 miles apart and walk towards each other along

Question

Stacy and Heather are 20 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?

A)7 mile
B)8 mile
C)9 mile
D)10 mile
E) 12 mile

A. 7 mile
B. 8 mile
C. 9 mile
D. 10 mile
E. 12 mile

TeamGMATIFY · Accepted Answer

In the time, speed distance problems, it is better to write down the information first. Stacy heather.jpg Distance traveled by Stacy in 24 minutes = 6*(24/60) = 2.4 miles For the rest of the distance, we can use the concept of relative speed to find out after how much time will they meet Since both are walking in the same direction, we will add the speeds. Therefore they will meet after 17.6/11 hours = 1.6 hours Distance travelled by Heather in 1.6 hours = 5*1.6 = 8 miles. Option B

ENGRTOMBA2018 · Answer

Good question to practice translation of word problems into actual equations.

Original distance between S and H = 20 miles.

Speed of S = 5+6 = 6 mph, Speed of H = 5 mph.

Time traveled by H = t hours ---> time traveled by S = t+24/60 = t+2/5 hours.

Now, the total distances traveled by S and H = 20 miles ---> 6*(t+2/5)+5*t=20 ---> t= 8/5 hours. Thus H has traveled for 8/5 hours giving you a total distance for H = 5*8/5 = 8 miles.

B is thus the correct answer.

Hope this helps.

P.S.: based on the wording of the question, you should calculate "how far from the  original destination has Heather walked  when the two meet". 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.

tuandoan92 · Answer

After 24 mins, Stacy travel 24/60*6=2.4m -> 6*t+5*t=20-2.4=17.6 -> t=17.6/11 -> Distance = 17.6/11*5=8
-> Answer B

rsh12 · Answer

A lot of ways to solve this problem have already been discussed. The following is my way of solving it:

Stacy
Time Speed distance
X+24 1/10(miles/min) 20-y

Heather
Time Speed distance
X 1/12(miles/min) y

Thus,

Two equations formed by Speed = Distance/time
Y=8 miles.

ShivamoggaGaganhs · Answer

After 24 min, stancy travels 2.4

Now, distance becomes 17.6

Thus,

D=17.6/11 *5=8 m

sarphant · Answer

Since Stacey already covered a distance which is (6 mile/hr * 24 min) = 2.4 mile
The remaining distance is (20 - 2.4) = 17.6 mile which will be covered in 17.6 / 11(6+5) = 1.6 hr 
And, in that 1.6 hr H will cover 1.6 * 5 = 8 miles.

whatsarc · Answer

S________20miles_________H

H starts 24 mins late, so let's put H 24mins further away from S. In 24mins H travels 2 miles (move H 2 miles away)

New distance

S___________22miles________H
Now 22miles and speed is 11mph
They travel for 2 hours before meeting.

In 2 hrs H travels 10miles. (of which 2 was added for the sake of easier calculation) 
Effective travel is 8miles.

This approach helps avoid numbers like 17.6/11 etc.

Hope its helpful

luisdicampo · Answer

Deconstructing the Question  
Total Distance = 20 miles.
Heather's Speed ( R_h ) = 5 mph.
Stacy's Speed ( R_s ) = 5 + 1 = 6 mph.
Time Lag: Heather starts 24 minutes after Stacy.

Step 1: Handle the Head Start  
Convert 24 minutes to hours:  \frac{24}{60} = 0.4  hours.
Distance Stacy covers alone:  D_{start} = R_s 	imes t = 6 	imes 0.4 = 2.4  miles.

Remaining Distance between them when Heather starts:
 D_{rem} = 20 - 2.4 = 17.6  miles.

Step 2: Calculate Meeting Time  
Since they are moving towards each other, add their speeds.
Relative Speed =  6 + 5 = 11  mph.

Time to meet ( t ) =  \frac{Distance}{Relative Speed} = \frac{17.6}{11} = 1.6  hours.

Step 3: Calculate Heather's Distance  
Heather walked for exactly 1.6 hours.
Distance =  Rate 	imes Time 
Distance =  5 	imes 1.6 = 8  miles.

Answer:  B

Stacy and Heather are 20 miles apart and walk towards each other along

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

Stacy and Heather are 20 miles apart and walk towards each other along

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia