Question 62724
{{{(600/t1)-10=600/(t2)}}}
Correct but things go pear shaped in the next line
{{{(600/t2)-(10*t2)=(600*t1)}}}
Should be multiply both sides by t2 to get
{{{(600t2/t1)-(10*t2)=(600)}}}
Multiply both sides by t1 to get
{{{(600t2)-(10*t1t2)=(600t1)}}}
Don't forget that t1 + t2=22 hours so t2=22-t1
{{{600(22-t1)-10*t1(22-t1)=(600t1)}}}
{{{13200-600t1-220t1+10t1^2=600t1}}}
{{{10t1^2-820t1 +13200=600t1}}}
{{{10t1^2-1420t1 +13200=0}}}
{{{t1^2-142t1 +1320=0}}}
{{{(t1-10)(t1-132)=0}}}
ie t1=10 hours or t1 = 132 hours
The second answer is not practical (return trip in -110 hours) so the first part of the trip took 10 hours(at an average speed of 60 mph) and the second part 12 hours(at an average speed of 50 mph).