Question 562018
A train travels from city A to city B and then to city C.
 The distance from A to B is 51 miles and the distance from B to C is 75 miles.
 the average velocity from A to B was 35mph and the average velocity from B to C was 50mph. 
What was the average velocity from A to C in miles per hour?
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The total distance: 51 + 75 = 126 mi
:
Let a = average for the whole trip
:
Write a time equation; time = dist/speed
:
AB time + BC time = AC time
{{{51/35}}} + {{{75/50}}} = {{{126/a}}}
Multiply by 350a to clear denominators, results
10a(51) + 7a(75) = 350(126)
510a + 525a = 44100
1035a = 44100
a = {{{44100/1035}}}
a = 42.6 mph av for AC
:
:
Check;
{{{51/35}}} + {{{75/50}}} = {{{126/42.6}}}
1.457 + 1.5 = 2.947