SOLUTION: 19. A motorist travelled 115 km on an expressway at an average speed of 92 km/h and another 45 minutes on the other roads. If the average speed for his whole journey was 80 km/h, h

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Question 392213: 19. A motorist travelled 115 km on an expressway at an average speed of 92 km/h and another 45 minutes on the other roads. If the average speed for his whole journey was 80 km/h, how far did he travel on the other road?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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19. A motorist traveled 115 km on an expressway at an average speed of 92 km/h
and another 45 minutes on the other roads.
If the average speed for his whole journey was 80 km/h, how far did he travel on the other road?
:
Let d = distance on the other roads
:
Change 45 min to .75 hrs
:
Write a time equation: time = dist/speed
:
express time + road time = total time
115%2F92 + .75 = %28%28d%2B115%29%29%2F80
Find least common multiple
92: 2*2*23
80: 2*2*2*2*5
LCM: 2*2*2*2*5*23 = 1840
:
Multiply equation by 1840, results:
20(115) + .75(1840) = 23(d+115)
:
2300 + 1380 = 23d + 2645
:
3680 - 2645 = 23d
:
1035 = 23d
d = 1035%2F23
d = 45 miles on other roads
:
:
Check solution by finding the times (total dist 115 + 45 = 160 mi)
115/92 = 1.25 hrs
other rd= .75 hrs
-------------------
160/80 = 2.00 hrs