SOLUTION: Can you please help me with this uniform motion problem? If the speed were increased by 10mph, a 420 mile trip would take 1 hr less time. How long will the trip take at the slower

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Question 211587This question is from textbook
: Can you please help me with this uniform motion problem? If the speed were increased by 10mph, a 420 mile trip would take 1 hr less time. How long will the trip take at the slower speed? Please show me all the steps and please get back to me before Tues. 10am.
Thank you guys This question is from textbook

Found 2 solutions by vleith, scott8148:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Distance+=+Rate%2ATime
You are told the distance is 420 miles.
Let the slow speed be represented by s (in miles per hours) and the slow time be represented by t (in hours)
So 420+=+s+%2A+t
Thus 420%2Ft+=+s
You are told that at s%2B10, the time will be t-1
So 420+=+%28s%2B10%29%28t-1%29
Now substitute in the value you found for s above
420+=+%28%28420%2Ft%29+%2B+10%29+%2A+%28t-1%29
420+=+%28420%2B10t%29%2Ft+%2A+%28t-1%29
420t+=+%28420%2B10t%29+%2A+%28t-1%29
420t+=+420t++-420+%2B+10t%5E2+-10t
0+=+10t%5E2+-10t+-+420
0+=+t%5E2+-+t+-42 factor this or use the quadratic equation
0+=+%28t-7%29%28t%2B6%29
For a product to equal 0, one or more of the terms multiplied must be 0. So
either t-7=0 ot t%2B6+=+0 that means either
t=7 or t=-6 since the time cannot be negative, the time at the slow speed must be 7 hours.
Now check your answers. If the time is 7 hours then the slow speed must be 60mph
If the speed if 10mph faster, then the faster speed is 70mph.
At 70mph, the time is 420/70 = 6 hours. Which is an hour faster.
So there you have it.
happy Labor day -- and still int time for 10am tomorrow

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
rate = distance / time

rate + 10 = distance / (time - 1)

(distance / time) + 10 = distance / (time - 1) ___ (420 / t) + 10 = 420 / (t - 1)

(420 + 10t) / t = 420 / (t - 1)

multiplying by t(t - 1) ___ 10t^2 + 410t -420 = 420t

subtracting 420t and dividing by 10 ___ t^2 - t - 42 = 0

factoring ___ (t + 6)(t - 7) = 0

t + 6 = 0 ___ t = -6 ___ negative value not realistic

t - 7 = 0 ___ t = 7