Dalileh and Lila set out on their bicycles in opposite

Question

Dalileh and Lila set out on their bicycles in opposite directions at 5:00 PM at constant speeds of 30 and 20 kilometers per hour respectively. Two hours later, their father set out to pick them up. He picked up Dalileh and then picked up Lila, and finally returned home with both. If the time spent picking up each was negligible, at what time did they arrive home if their father drove at a constant speed of 120 km/h?

(A) 8:40 (B) 8:50 (C) 9:00 (D) 9:10 (E) 9:40

ArvGMAT · Answer

Let's see

In 2 hours Dalih covers 60 KM
30 minutes for dad to pick him up
Lila is 50*2 = 100 km away
At Dad's speed that is 100/120 = 5/6 hours
To come back it is 40 km away or 40/120 = 1/3 hours
total time spent = 120+30+50+20 = 220 min.
i.e.
8:40 pm
A

Professor · Answer

after two hours, D is 60 kms and L is 40 KM far from home. D passes (60+x)/120 = x/30 => x = 20 kms when F meets D. and they will be 60+20 = 80km farther from the home. it takes F and D 40 minuets to cover 80 kms and 20 kms respectively. in 40 minuets, L passes 20x20/60 = 13.33 kms. at the same time, L will be 53.33 (40 + 13.33) kms farther from home and 133.33 (80 + 40 + 13.33) kms farther from F and D. L passes (133.33 +x)/120 = x/20 => x = 26.67 kms when F and D meet L. it takes F (along with D) and L, each, 80 minuets to cover a distance of 160 kms and 26.67 kms respectively. when they all meet, they are 80 (40+13.33+26.67) kms away from the home. so it takes F (along with D and L) 40 minuets to come back home covering 80 kms. so total times taken = 2 hours + 40 minuets + 80 minuets + 40 minuets.. i.e 9.40. :roll:

again where did i miss????????

v1rok · Answer

I am not going to repeat my calcs here, but I got 9:40pm too as my answer (and I swear I worked independently from Professor.)

So, is it 9:40?

rdw28 · Answer

I actuallly got 9:40 (9:45 the first time, but i checked my work). The professor has it right on the nose


I am not completly sure what my man Arv is mapping out.. Nentheless, It might very well be the right answer.

kevincan · Answer

The answer is indeed 9:40. I'm good at making up questions, but not so good at getting the answers :-D

. Sorry!

jaynayak · Answer

E 9.40

When father sets out to pick Dalleih, let x be the number of hours he takes to reach Dalleih.
(2+x)30 = 120x
x= 2/3

Hence total time taken from 5 pm till he reaches back to the starting point after picking up Dallieh = 2+ 2/3+2/3 = 10/3 hrs

Let the time taken from the starting point to when he picks up the other girl be y
(10/3 + y) 20 = 120y
y = 2/3

Hence total time taken to pick up both girls and return home =
10/3 + 2/3 + 2/3 = 14/3 Hrs

14/3 hrs = 280 mins = 4 hrs and 40 mins = 9.40

Professor · Answer

making so many quality questions is really a difficult but a wonderful job. you are doing great job for us. just a note: "specific answer is gmat feature".

thanks.

Zoelef · Answer

7pm, Dalileh is 60km west, Lila is 40km east from home.

in 40 minutes (2/3 hour), Dalileh travels another 20km west, while Dad travels 80km west and catches Dalileh.

Now, Lila is 53 1/3 km east + 80km from the start, so 133 1/3 km east of Dad.

in 20 min, Dad catches up by 40 km, while Lila nets 6 2/3 km east, a net loss of 33 1/3 km - Dad is 100 km away from Llia at 8:00. Lila is now 60 km from home. 

Dad catches up by 100km in one hour, so Dad meets Lila at 9:00, 80 km from home. 80/120 is 2/3 hour, so Dad returns home at 9:40. (E)

Only posting this since I missed the "go home" part the first time, oops.

Dalileh and Lila set out on their bicycles in opposite

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

My Rewards