SOLUTION: a certain space probe traveled at a speed of 1280 km/h, and then, by firing retro-rockets, slowed to 950 km/h. The total distance traveled was 75,300 km in a time of 63.5 hours.

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Question 78046: a certain space probe traveled at a speed of 1280 km/h, and then, by firing retro-rockets, slowed to 950 km/h. The total distance traveled was 75,300 km in a time of 63.5 hours. Find the distance from the starting point at which the retro-rockets were fired.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a certain space probe traveled at a speed of 1280 km/h, and then, by firing retro-rockets, slowed to 950 km/h. The total distance traveled was 75,300 km in a time of 63.5 hours. Find the distance from the starting point at which the retro-rockets were fired.
:
The distance from the starting point to where the retro-rockets were fired would
be the distance traveled at 1280 km/hr: Let that dist = d
Then:
(75300-d) = distance traveled at 950 km/hr
:
Write a time equation: Time = distance/speed
d%2F1280 + %28%2875300-d%29%29%2F950 = 63.5
:
Multiply equation by (1280)(950) to get rid of the denominators, you then have:
:
950d + 1280(75300 - d) = (1280)*(950)*(63.5)
:
950d + 96384000 - 1280d = 77126000
:
950d - 1280d = 77126000 - 96384000
:
-330d = -1916800
:
d = -1916800/-330
:
d = 58,085 km traveled when retro-rocket were fired
:
Distance traveled at the slower speed: 75300 - 58085 = 17215 km
:
Check solution by finding the time at each speed:
58085%2F1280 + 17215%2F950 =
:
45.4 + 18.1` = 63.5, confirms our solution