Sopwith Camel
Posted in Aircraft Model by admin
on March 7, 2009
I have a math quiz tomorrow?
Snoopy flies his Sopwith Camels from his base to his destination and back, a total of 240 miles. If he had flown 20 miles per hour faster, the trip would have taken an hour less. How fast did Snoopy fly?
I know i need to set up a system of equations but I don't know how to make the equation...help me please?
Let t hr be the time of his trip and u mph be his flying speed.
As speed * time = distance:
ut = 240 ...(1)
If he had flown 20 mph faster his speed would have been u + 20 mph.
As the trip would have taken an hour less, it would have taken time t - 1 hr.
The distance, however, is still 240 miles.
Therefore:
(u + 20)(t - 1) = 240 ...(2)
You are asked to find u. Therefore eliminate t from (1) and (2).
(1) gives t = 240 / u.
Substituting this in (2):
(u + 20)(240 / u - 1) = 240
Multiplying the brackets:
240 + 4800 / u - u - 20 = 240
4800 / u - u - 20 = 0
Multiplying by u:
4800 - u^2 - 20u = 0
u^2 + 20u - 4800 = 0
Factorising:
(u + 80)(u - 60) = 0
u = - 80 or u = 60.
Discarding the negative result, Snoopy flew at 60 mph.
Check it out.
From (1) t = 4 hr.
Flying 20 mph faster gives speed 80mph.
240 miles at 80 mph takes 3hr, which is an hour less.
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