practicealot wrote:
Two trucks travel from Alphaburg to Betaville along the same route. The speed limit for the first 30 miles is 60 miles per hour. The speed limit for the next 10 miles is 40 miles per hour, and the limit for the final 60 miles is 55 miles per hour. Truck F has a maximum speed of 70 miles per hour, but Truck S has a speed-limiting governor installed to cap its maximum speed at 50 miles per hour. Truck S departs Alphaburg 12 minutes before Truck F. If each truck travels at the lesser of the speed limit or the maximum speed of the truck, how far from Betaville is the point where Truck F catches up with Truck S?
A) 5 miles
B) 20 miles
C) 55 miles
D) 95 miles
E) Both trucks arrive at Betaville simultaneously
Another way would be take each stretch separately..
SO..
S travelling at 50 miles per hour covers 50/60*12=10 miles..
Let us work on each stretch..
(I) Stretch II does not have any difference as both travel at 40 mph..
(II) Stretch I has a difference of 10 mph ( relative speed -- 60 mph vs 50mph), so F will cover 5 miles in 30/60 hr . Hence S still has 10-5 miles over F, when F covers this 30 miles.
(III) In stretch III, there is a difference of 5 mph ( relative speed -- 55 mph vs 50mph), so F will cover remaining 5 miles over S in 1 hr . Hence S and F will meet 1 hr after F starts in third stretch. So, F will cover 55 miles in 1 hr at 55mph...
thus 60-55 or 5 miles short of finish point..
Simplified form now..
10 miles to cover
Stretch I.... F takes 30/60 or 1/2hr and covers (60-50)*1/2=5 miles, thus 5 miles remaining
Stretch II... No difference as both travel at 40mph
Stretch III.. F will cover 55-50 miles in 1 hr and as it has 5 miles to cover, another 1 hr travel by F or 55 miles.
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