speed and time word problem

Question

A truck begins a trip at noon. From noon until 345pm the truck travels with a speed of 45 miles per hour. From 345pm until the truck ends it's trip the truck travels with a speed of 55 mph. At what time does the truck end its trip if the average speed is 48mph?

Answer 1

truck: 45 mph, 12-3:45; 55mph, 3:45-?

avg. speed = 48 mph

 

solution method: guess and check

distance = rate times time

 

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Is the answer 4:45?
d1 = 45 mph times 3.75 hours = 168.75 miles
d2 = 55 mph times 1 hour = 55 miles
d = d1 + d2 = 223.75 miles

223.75 miles = avg. speed times 4.75 hours
avg. speed = 47.1 mph

 

Is the answer 5:45?

d1 = 45 mph times 3.75 hours = 168.75 miles

d2 = 55 mph times 2 hours = 110 miles

d = d1 + d2 = 278.75 miles

278.75 miles = avg. speed times 5.75 hours

avg. speed = 48.5 mph

 

Is the answer 5:15?

d1 = 45 mph times 3.75 hours = 168.75 miles
d2 = 55 mph times 1.5 hours = 82.5 miles
d = d1 + d2 = 251.25 miles
251.25 miles = avg. speed times 5.25 hours
avg. speed = 47.9 mph

 

Is the answer 5:30?

d1 = 45 mph times 3.75 hours = 168.75 miles
d2 = 55 mph times 1.75 hours = 96.25 miles
d = d1 + d2 = 265 miles
265 miles = avg. speed times 5.5 hours
avg. speed = 48.2 mph

 

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The truck ends its trip between 5:15 and 5:30.

Can you find the exact time using algebra?

Answer 2

The distance covered by the truck when traveled noon to 3:45pm:

 

time = 3hr and 45 min = 3.75hr

velocity = 45 mph

velocity = distance/time

distance = velocity x time = 45 x 3.75 = 168.75 miles

 

Let as assume the time that the truck traveled after 3:45pm is t:

 

Therefore, the distance traveled by the truck after 3:45pm is:

 

distance = velocity x time = 55 x t = 55t     (1)

 

But the average speed is total distance/ total time,

 

48 = (168.75 + 55t)/(3.75 + t)

180 + 48t = 168.75 + 55t

 

t = 1.61 hr  (means 1 hr 0.61 (60) min = 1hr and 36 min)

 

Therefore, the truck ended its trip 3:45pm + 1hr and 36min is 5:21pm