On his trip to Alaska, Joe traveled y percent of the total distance at

Question

On his trip to Alaska, Joe traveled y percent of the total distance at an average speed of 50 miles per hour and the rest of the distance at an average speed of 70 miles per hour. What was Joe’s average speed in miles per hour for the whole trip in terms of y?

(A) 70(50 – y)

(B) (y + 60)/4

(C) 10,000 – 199y

(D) 17,500/(y + 250)

(E) y/2 + 35

If the first part is at 50 mile/h and the second part is 70 miles/h the overall speed is the toral distance / total time.

Pick a number for distance we can use 350. so the time for first part is 7 and for the rest is 5.

in the end we will have 26. something, but testing answer choices nothing comes up

(

where I'm wrong

PS: I could use a bit of logic and come to the answer easier, but .............

( where I'm wrong PS: I could use a bit of logic and come to the answer easier, but .............

Bunuel · Accepted Answer

Say y=100%, so say Joe traveled entire trip at an average speed of 50 miles per hour. So, in this case we'd have that his average speed is simply 50 miles per hour.

Now, plug y=100 into the answer choices and see which one yields 50. Only answer choice D fits.

Or:  say y=0%. In this case we'd have that Joe's average speed is 70 miles per hour.

Now, plug y=0 into the answer choices and see which one yields 70. Again, only answer choice D fits.

Answer: D.

Hope it helps.

BangOn · Answer

As you need a quick logical answer let me try
Lety distance be X
so Time 1 = XY/100*50 
Time 2 = X(100-Y)/100*70

Avg Speed = Total Distance / Total Time
= X/ Time 1 + Time 2

Ans D
reason is simple...X cancels and Y reamins in denominator
only 1 option has the same

HiteshPunjabi · Answer

I deducted the above within 30 secs but took another 3 mins

to solve the whole mess to get to the ans choice. As you rightly said if we notice Y remains in deno for only one choice, life becomes easier. I tend to go the conventional way every time not the GMAT way

Any other tricks like this which could help save TIME?

HiteshPunjabi · Answer

Another way - less than 2 mins
Take Total distance = 100
1) y% of 100 at 50 mi/hr = distance is y miles -- So its y miles at 50 mi/hr
2) remaining (100-y) miles at 70 mi/hr

Avg spd = Total Dist/Total Time = 100/(y/50 + (100-y)/70) -> leads to D.(in case there are more choices with y in deno)

Bunuel · Answer

Check here: on-his-trip-to-alaska-joe-traveled-y-percent-of-the-total-141661.html#p1140444

rajathpanta · Answer

i just plugged in some random nos-

say Total distance=100
 y=30%
Then ball parked to find that D is the ans.

Bunuel · Answer

If you plug y=0 or y=100, then you won't need to plug anything for the distance. Check here: on-his-trip-to-alaska-joe-traveled-y-percent-of-the-total-141661.html#p1138511

kheba · Answer

No need to assume the value of y. Assume total distance = 100. Therefore total time taken = (y/50) + (100-y)/70 = (y + 250)/175

Average speed = 100/( (y + 250)/175) = 175000/ (y + 250)

sumert · Answer

I recently encountered one such questions and couldn't come up with the logic to start the solution.
After solving a bunch of these, the quickest method (at least for me) is to calculate the individual times and then divide the total distance (Which I assume 100 in most cases) with the total time. A little bit of calculation but it works better than plugging in numbers for me.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

On his trip to Alaska, Joe traveled y percent of the total distance at

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

On his trip to Alaska, Joe traveled y percent of the total distance at

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