A man covers the first 5 miles of the journey at a rate of 25 miles per hour, the next 10 miles at a rate of 30 miles per hour and finally the remainig distance in 30 minutes, thereby averaging 25 miles per hour for the entire journy. Approximately how much is the distance travelled in the last phase for the journey?
A. 9
B. 10
C. 11
D. 15
E. 20
The OA is C.
I know that speed = dist / time, then
The total average speed is 25 miles per hour.
The total time will be, 1/5 hr + 1/3 hr + 1/2 hr (30 minutes) = 31/30 hr.
The total distance will be, 15 mile + d miles.
Total speed = total distance / total time
$$25=\frac{15+d}{\frac{31}{30}}\ then\ \ d=\frac{65}{6}=10.8\approx11\ miles$$
Experts, any sugestion about how to solve this PS question? Thanks.
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A man covers the first 5 miles of the journey at the rate...
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BTGmoderatorLU
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Your solution is perfect!LUANDATO wrote:A man covers the first 5 miles of the journey at a rate of 25 miles per hour, the next 10 miles at a rate of 30 miles per hour and finally the remainig distance in 30 minutes, thereby averaging 25 miles per hour for the entire journy. Approximately how much is the distance travelled in the last phase for the journey?
A. 9
B. 10
C. 11
D. 15
E. 20
The OA is C.
I know that speed = dist / time, then
The total average speed is 25 miles per hour.
The total time will be, 1/5 hr + 1/3 hr + 1/2 hr (30 minutes) = 31/30 hr.
The total distance will be, 15 mile + d miles.
Total speed = total distance / total time
$$25=\frac{15+d}{\frac{31}{30}}\ then\ \ d=\frac{65}{6}=10.8\approx11\ miles$$
Experts, any sugestion about how to solve this PS question? Thanks.
Cheers,
Brent
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Jeff@TargetTestPrep
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The first part of the journey takes 5/25 = 1/5 hour, the second part takes 10/30 = 1/3 hour, and the final part takes 1/2 hour.LUANDATO wrote:A man covers the first 5 miles of the journey at a rate of 25 miles per hour, the next 10 miles at a rate of 30 miles per hour and finally the remainig distance in 30 minutes, thereby averaging 25 miles per hour for the entire journy. Approximately how much is the distance travelled in the last phase for the journey?
A. 9
B. 10
C. 11
D. 15
E. 20
Let's represent the distance travelled in the last phase for the journey by d.
We can use the average rate formula:
Average rate = total distance/total time
25 = (5 + 10 + d)/(1/5 + 1/3 + 1/2)
25 = (15 + d)/(6/30 + 10/30 + 15/30)
25 = (15 + d)/(31/30)
25 = (450 + 30d)/31
775 = 450 + 30d
325 = 30d
11 ≈ d
Answer: C
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