SOLUTION: Two planes just toke off a mountain. The first plane is travelling 1.5 times as fast as the second one. After travelling in the same direction for eight hours they are for 420 mile

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Question 1052086: Two planes just toke off a mountain. The first plane is travelling 1.5 times as fast as the second one. After travelling in the same direction for eight hours they are for 420 miles apart. What is the average speed of Each plane
Found 2 solutions by addingup, josmiceli:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
rt = d (rate*time = distance)
r = d/t
8x(1.5) = 8x+420
12x = 8x+420
4x = 420
x = 105 was the speed of the slow plane, and
105*1.5 = 157.5 was the speed of the fast plane
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Check - In 8 hours:
157.5*8 = 1260
105*8 . = 840
Difference:420 Correct
:
John

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I assume they take off at the same time.
Let +s+ = the speed in mi/hr of the slower plane
+1.5s+ = the speed of the faster one
+d+ = distance in miles the faster one travels
+d+-+420+ = distance in miles the slower one travels
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Equation for slower one:
(1) +d+-+420+=+s%2A8+
Equation for faster one:
(2) +d+=+1.5s%2A8+
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Substitute (2) into (1)
(1) +1.5%2A8s+-+420+=+8s+
(1) +12s+-+420+=+8s+
(1) +4s+=+420+
(1) +s+=+105+ mi
and
+1.5s+=+157.5+ mi
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The speed in mi/hr of the slower plane is 105 mi/hr
The speed of the faster plane is 157.5 mi/hr
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check:
(1) +d+-+420+=+105%2A8+
(1) +d+=+840+%2B+420+
(1) +d+=+1260+ mi
and
(2) +d+=+1.5%2A105%2A8+
(2) +d+=+1260+ mi
OK