Problema Solution
Car A can travel 250 miles in 3 hours less time than it takes car B to travel 440 miles. The rate of car B is 5 miles per hour faster than that of car A. Find the rates of both cars.
Answer provided by our tutors
lets call everything of car A as one(1) and car B as two(2),
we can get Distance, Rate and Time.
D1=250,
R1=R2-5 ( cuz Rate of B is 5 faster, hence subtraction)
T1=T2-3 ( cuz A takes 3 less than B, so subtraction from B)
D2=440
R2
T2
Distance=RatexTime
Car A: 250=(R2-5)(T2-3) -------eqA
Car B: 440=R2T2 ------------EqB
so simplifying Car A equation:
250= R2T2 -3R2 -5T2 +15
since 440=R2T2, we get,
250 = 440 -3R2-5T2 + 15
3R2+5T2=165 --------------EQ 1
T2=440/R2 [from EqB]
so we get,
3R2 +5(440/R2) =165
simplifying we get,
3R2 + (2200/R2) =165
3R22 +2200=165R2
3R22 -165R2 +2200=0
using quadratic formula, we get R2= 32
R1=R2-5 so R1=27
Hope this helps
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