rate problem :9

[maus]

Thanks in advance!

Carlos drives from home to work at an average rate of 22 mph in 9 minutes. If he bikes the same route at an average of 6 mph how long does it take him to bike the same route?



*for whatever reason my brain cant seem to comprehend this...any tips on how to recognize these things? I have been studying the word translation problems in the MGMAT book but have a hard time recognizing these problems and knowing what to do with the parts on the test...

[Frankenstein]

Hi,
Avg speed= Distance/time => distance = speed*time.
As distance is same in both the cases, we equate them.
22*9 = 6*t => t =33 mins

[MBA.Aspirant]

He goes from home to work covering a distance of 22 *9= 198 miles

Goes back the same route with 6 mph in 198/6 = 33 mintues

[Whitney Garner]

He goes from home to work covering a distance of 22 *9= 198 miles

Goes back the same route with 6 mph in 198/6 = 33 mintues

Be careful with the language, he is traveling 22 miles per HOUR for 9 MINUTES. So the correct time would be 9/60 hours or 3/20 hours. Therefore the distance is 22(3/20) = 33/10 = 3.3 miles.

The time it would take to do 3.3 miles at only 6 mph would be:
3.3 = 6(t)
t = 0.55 hours = 33 minutes

@Frankenstein provided a shortcut (avoiding the fractions) but we still want to be really careful with the units:

Distance = Rate x Time (for the car trip)
D = 22 x (9/60) <--to convert 9 minutes to hours


Distance = Rate x Time (for the bike trip)
D = 6 x (t minutes/60) <--to convert t minutes to hours

Because the D's are the same:
22 x (9/60) = 6 x (t minutes/60)

Multiply both sides times 60 and we have the equation:
22(9) = 6(t)
t = 22(9)/6 = 11*3 = 33 minutes


Whit

[MBA.Aspirant]

Thanks Whit - I took note of that, did the conversion and got the same answer

Btw you're a skydiver right? that's cool

[Frankenstein]

@Frankenstein provided a shortcut (avoiding the fractions) but we still want to be really careful with the units:

Whit

Hi,
I didn't want to do the fraction part. So, deliberately avoided them to keep the solution simple.

[iamsaurav]

Hi

This is a Ratio and proportion problem. Since, we know there is an inverse relation between speed an time we use it and et to our results as follows :

22/6=x/9

find x. Hence your answer.

[cans]

22mph 9 minutes.
distance = 22*9/60 = 3.3m
speed of bike=6mph
time=3.3/6 hours = 33 minutes