The Ryder family trave1ed at an average rate of 60 miles per hour(mph)

Question

The Ryder family traveled at an average rate of 60 miles per hour(mph), and it took 10 hours to complete their trip. If they trave1ed for 4 of their 10 hours at a constant speed of 70 mph, at what average speed did they trave1 for the remaining 6 hours to obtain the 60 mph average for the entire trip?

A. 53 1/3 mph
B. 53 2/3 mph
C. 54 1/3 mph
D. 55 1/3 mph
E. 55 2/3 mph

A. 53 1/3 mph
B. 53 2/3 mph
C. 54 1/3 mph
D. 55 1/3 mph
E. 55 2/3 mph

Mona2019 · Answer

Average speed is distance travelled/time taken
 \frac{(4*70 + 6*x) }{10}=60

x =\frac{160}{3}=53*\frac{1}{3}

IMO A

IanStewart · Answer

You could use weighted average principles here, since average speed is a weighted average, weighted by time (and a bit unusually for an average speed problem, this question gives us all of our times). But doing that doesn't save much time, because the numbers don't work out too cleanly, and it's straightforward just to work out our remaining distance and time. In 10 hours at 60 mph, the distance traveled is 600 miles. In 4 hours at 70 mph, the distance traveled is 280 miles. So the remaining 320 miles were covered in 6 hours, at a speed of 320/6 = 160/3 = 53 1/3 mph.

Target4bschool · Answer

IanStewart  could you please show how to do it with weighted average?

Posted from my mobile device

IanStewart · Answer

Using alligation, you'd draw this number line:

---A-------60-----------------70----

and because the times are in a 4 to 6, or 2 to 3 ratio, the distances to the middle average are in a 2 to 3 ratio. Since the larger distance is 10, the smaller distance is thus 2/3 of that, or 20/3, and A = 60 - (20/3) = 53 1/3.

That's a weighted average solution using alligation -- if you solve weighted average problems algebraically, the solution would essentially be the one I posted above.

gmatcafe · Answer

4*70+6*x=60*10
280+6x=600
6x=320
3x=160
x=53 1/3  A)

The Ryder family trave1ed at an average rate of 60 miles per hour(mph)

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

GMAT Problem Solving (PS) Questions

The Ryder family trave1ed at an average rate of 60 miles per hour(mph)

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

My Rewards