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Sanjana jogged uphill for a while at an average speed of 3 m

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Sanjana jogged uphill for a while at an average speed of 3 m

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Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles

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Anaira Mitch wrote:
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles
Let's start with a "Word Equation"
(distance traveled uphill) + (distance traveled downhill) = TOTAL DISTANCE

Let t = the time spent jogging UPHILL (in hours)
The total travel time = 40 minutes = 2/3 HOURS
So, 2/3 - t = the time spent jogging DOWNHILL (in hours)

Distance = (speed)(time)
So, we can rewrite our word equation as: 3t + 8(2/3 - t) = (4)(2/3)
Expand to get: 3t + 16/3 - 8t = 8/3
Subtract 16/3 from both sides to get: 3t - 8t = -8/3
Simplify to get: -5t = -8/3
Solve: t = (-8/3)/(-5) = 8/15
So, Sanjana spent 8/15 hours traveling UPHILL

How far did Sanjana jog uphill?
Distance = (speed)(time)
So distance = (3)(8/15) = 8/5 = 1 3/5 miles

Answer: D

Cheers,
Brent

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Answer is D

The total distance travelled in 40 minutes at average speed of 4 miles per hour is : 4*(40/60) = 8/3 miles.
Now, let she jogged for x hours uphill, so time consumed jogging downhill will be (40/60)-x hours= (2/3)-x22/3
/
Since total distance = distance uphill+ distance downhill
=> 8/3= 3*x + 8* [(2/3)-x]
x=8/15
Now, distance jogged uphill= 3*x=3*8/15=13/5= 1 3/5
Hence D

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Can this question be solved using any other approach apart from algebra?

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Anaira Mitch wrote:
Can this question be solved using any other approach apart from algebra?
You could also try testing the answer choices.

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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Thanks Brent.

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Quote:
Quote:
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles
Can this question be solved using any other approach apart from algebra?
This is a MIXTURE problem.
Two speeds (3 mph and 8 mph) are combined to form a mixture with an average speed of 4 mph.
To determine how much time must be spent at each speed, we can use ALLIGATION.
Let U = the uphill speed and D = the downhill speed.

Step 1: Plot the 3 speeds on a number line, with the speeds for U and D on the ends and the speed for the mixture in the middle.
U 3---------4----------8 D

Step 2: Calculate the distances between the values on the number line.
U 3----1----4----4----8 D

Step 3: Determine the time ratio for the two speeds.
The time ratio for U and D is equal to the RECIPROCAL of the distances in red.
U : D = 4:1.

Implication:
Of every 5 minutes of travel time, 4 minutes are spent at the uphill speed, while 1 minute is spent at the downhill speed.

Thus, 4/5 of the total travel time is spent at the uphill speed:
(4/5)(40 minutes) = 32 minutes = 32/60 hour = 8/15 hour.
Since 8/15 hour is spent at the uphill speed of 3 mph, we get:
Distance uphill = rt = (3)(8/15) = 8/5 = 1 3/5 miles.

The correct answer is D.

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Anaira Mitch wrote:
Sanjana jogged uphill for a while at an average speed of 3 miles per hour, then jogged downhill for a while at an average speed of 8 miles per hour. If Sanjana jogged the uphill and downhill stretches in a total of 40 minutes at an average speed of 4 miles per hour, how far did she jog uphill?

A. 1 mile
B. 1 1/3 miles
C. 1 1/2 miles
D. 1 3/5 miles
E. 1 2/3 miles
We can let t = the number of hours Sanjana jogged uphill. Since 40 minutes = 2/3 of an hour, the time she jogged downhill was (2/3 - t) hours. We can create the equation:

3t + 8(2/3 - t) = 4(2/3)

3t + 16/3 - 8t = 8/3

-5t = -8/3

t = 8/15

Since she jogged 8/15 of an hour uphill at an average speed of 3 mph, she jogged 8/15 x 3 = 8/5 = 1 3/5 miles.

Answer: D

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scott@targettestprep.com



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