Question 1204831
<br>
a) time = distance/speed: {{{4950/x}}}<br>
b) time = distance/speed: {{{4950/(x-50)}}}<br>
c) time return trip at lower speed was 4 hours longer: {{{4950/(x-50)=4950/x+4}}}<br>
d) Solve the equation....<br>
{{{4950/(x-50)=4950/x+4}}}<br>
Clear fractions by multiplying by {{{(x)(x-50)}}}<br>
{{{4950x=4950(x-50)+4(x^2-50x)}}}
{{{4x^2-200x-247500=0}}}
{{{x^2-50x-61875=0}}}<br>
Trying to solve that equation by factoring will take a long time; possibly the best way to finish the problem is to use a graphing calculator or some other tool.<br>
Or here is an algebraic technique that you can use to work this kind of problem.<br>
We are looking for two numbers whose difference is 50 and whose product is 61875.<br>
Let the two numbers that differ by 50 be y+25 and y-25.  Then<br>
{{{(y+25)(y-25)=61875}}}
{{{y^2-625=61875}}}
{{{y^2=62500}}}
{{{y=250}}}<br>
The two speeds are y+25 = 275 km/h and y-25 = 225 km/h.<br>
ANSWER: the speed of the plane in still air is 275 km/h.<br>
e) 4950/275 = 18; 4950/225 = 22; total time 18+22 = 40 hours.<br>