Question: Jake rides his bike for the first 2/3 of the distance from home to school, traveling at 10 miles per hour. He then walks the remaining 1/3 of the distance at 3 miles per hour. If his total trip takes 40 minutes, how many miles is it from Jake's home to his school?
- 5/4
- 15/4
- 5
- 6
- 10
“Jake rides his bike for the first 2/3 of the distance from home to school”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
Given:
- Jake rides his bike for the first 2/3 of the distance from home to school at 10 mph
- He walks the remaining 1/3 distance at 3 mph
- Total travel time is 40 minutes or 2/3 hours
To find:
- The distance between Jake’s home to his school
Approach and Working:
If we assume the total distance to be x miles, we can write
- Distance travelled in bike = 2x/3 miles
Hence, the time for travel by bike = (2x/3)/10 hours
This comes down to x/15 hours. - Distance travelled by walking is x/3 miles.
Therefore, the time for walking taken is (x/3)/3 hours
This comes down to x/9 hours.
Since the total time of travel is ⅔ hours, the equation comes down to:
x/15 + x/9 = ⅔ hours
=> 8x/45 = ⅔
=> x= 90/24
=> x= 15/4 miles.
Correct Answer: B
Approach Solution 2:
Using the formula of average speed = ((p+q)*(ab)) (qa+pb)
P:q is the ratio of the distances traveled
Speeds at which the respective distances are traveled are a and b
Jake rides his bike for the first 2/3rd of the distance and
the remaining 1/3rd of the distance on foot,
making the ratio of the distances 2:1(p:q)
Jake travels by bike at speed(a)=10mph and travels by foot at speed(b)=3mph
Substituting values of a,b,p, and q, we get the value for the average speed, as follows
Average speed = ((2+1)*(10*3)) (10+6)
=> (3*30) 16
=>45/8
Therefore, the distance traveled by Jake is 40/60 * 45/8
=> 15/4
Correct Answer: B
Approach Solution 3:
The average speed formula is ((p+q)*(ab)) (qa+pb)
P:q is the ratio of travelled distances.
The corresponding lengths are covered at speeds a and b.
For the first two thirds of the route, Jake pedals his bike and
walking the final third of the journey,
Increasing the distances by a factor of 2:1 (p:q)
Jake moves at a speed of 10 mph on his bike and 3 mph on foot.
We obtain the average speed by substituting the values of a, b, p, and q.
Speed on average is ((2+1)*(10*3)) (10+6)
=> (3*30) 16
=>45/8
As a result, Jake travelled a distance of 40/60 * 45/8.
=> 15/4
Correct Answer: B
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