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22 Oct 2023, 16:40
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82% (02:11) correct
18%
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A truck left City M and traveled toward City N. A second truck left City N exactly 1 hour later and traveled toward City M. The trucks passed each other after they had traveled, nonstop, a combined total of 490 miles. If the average speeds of the trucks up to the time they passed each other were 50 miles per hour (mph) and 60 mph, respectively, how far, to the nearest mile, had the first truck traveled when the trucks passed each other?
A. 223
B. 240
C. 245
D. 250
E. 300
Truck.png [ 65.1 KiB | Viewed 8049 times ]
A. 223
B. 240
C. 245
D. 250
E. 300
Attachment:
Truck.png [ 65.1 KiB | Viewed 8049 times ]
22 Oct 2023, 18:58
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nick13
A truck left City M and traveled toward City N. A second truck left City N exactly 1 hour later and traveled toward City M. The trucks passed each other after they had traveled, nonstop, a combined total of 490 miles. If the average speeds of the trucks up to the time they passed each other were 50 miles per hour (mph) and 60 mph, respectively, how far, to the nearest mile, had the first truck traveled when the trucks passed each other?
a. 223
b. 240
c. 245
d. 250
e. 300
a. 223
b. 240
c. 245
d. 250
e. 300
Let's assume that the speed of the first truck (\(s_1\)) = 50 mph
The speed of the second truck (\(s_2\))= 60 mph
Distance covered by the first truck when the second truck begins its journey = 50 miles
Remaining distance = 490 - 50 = 440 miles
The ratio of the distance covered by the two trucks is in the ratio of their speeds
\(\frac{s_1}{s_2} = \frac{50}{60} = \frac{5}{6}\)
Hence, out of the 11 parts of the journey, the second truck covers 6 parts, and the first truck covers 5 parts.
Distance covered by the first truck = \(\frac{440}{11} * 5 = 200\)
Total distance covered = \(200 + 50 = 250\)
Option D
30 Mar 2024, 21:57
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nick13
A truck left City M and traveled toward City N. A second truck left City N exactly 1 hour later and traveled toward City M. The trucks passed each other after they had traveled, nonstop, a combined total of 490 miles. If the average speeds of the trucks up to the time they passed each other were 50 miles per hour (mph) and 60 mph, respectively, how far, to the nearest mile, had the first truck traveled when the trucks passed each other?
A. 223
B. 240
C. 245
D. 250
E. 300
Truck 1 Distance: R x T --- > 50 x (t + 1) = 50t + 50A. 223
B. 240
C. 245
D. 250
E. 300
Attachment:
Truck.png
Truck 2 Distance: R x T --- > 60t
Combined Distance of both trucks = 50t +50 + 60t = 490 miles
110t + 50 = 490
110t = 440
t = 4
Distance of truck 1: 50(4) + 50 = 200 +50 = 250 miles
Option D
