SOLUTION: Richard took a 1900km trip traveling by bus and plane. The bus averaged 60km/h and the plane averaged 700 km/h if the trip took a total of 5 h how many kilometers did she travel

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Question 1045761: Richard took a 1900km trip traveling by bus and plane. The bus averaged 60km/h and the plane averaged 700 km/h if the trip took a total of 5 h how many kilometers did she travel
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance traveled by bus in km
+1900+-+d+ = the distance traveled by plane
Let +t+ = time in hrs spent traveling by bus
+5+-+t+ = time in hrs spent traveling by plane
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Equation for bus:
(1) +d+=+60t+
Equation for plane:
(2) +1900+-+d+=+700%2A%28+5+-+t+%29+
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(1) +t+=+d%2F60+
Plug this result into (2)
(2) +1900+-+d+=+700%2A%28+5+-+d%2F60+%29+
(2) +1900+-+d+=+3500+-+%2835%2F3%29%2Ad+
(2) +5700+-+3d+=+10500+-+35d+
(2) +32d+=+4800+
(2) +d+=+150+
and
+1900+-+d+=+1900+-+150+
+1900+-+d+=+1750+
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She traveled 150 km by bus and 1750 km by plane
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check:
(1) +t+=+d%2F60+
(1) +t+=+150%2F60+
(1) +t+=+2.5+ hrs by bus
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(2) +1900+-+d+=+700%2A%28+5+-+t+%29+
(2) +1900+-+150+=+700%2A%28+5+-+t+%29+
(2) +1750+=+700%2A%28+5+-+t+%29+
(2) +5+-+t+-+2.5+ by plane
+2.5+%2B+2.5+=+5+ hrs total
OK