John drove part of a 260 km trip at 80 km/h and the rest at 100 km/h. Find the distance he traveled at 80 km/h if his total driving time was 2 h and 30 min.
Can somebody please explain why this is no solution????

Question

John drove part of a 260 km trip at 80 km/h and the rest at 100 km/h. Find the distance he traveled at 80 km/h if his total driving time was 2 h and 30 min.
Can somebody please explain why this is no solution????

anonymous · Answer

The total distance is 260 
Let the distance travel at 80kph=x 
Then distance travel for 100kph=(260-x) 
From D=RT, T=D/R 
For 80kph segment, T=x/80 
For 100kph segment, T=(260-x)/100 
Total time=2.5 hrs 
Therefore 
x/80 + (260-x)/100=2.5 
Multiply all terms by 400 
5x+4(260-x)=1000 
5x+1040-4x=1000 
x=-40 km!!! 
This is a stupid answer, and something is wrong. 
Look, if he drove the whole trip at 100kph, after 2.5 hours he has gone 
250km. And time is up. He's still 10 km short of his destination. 
There's some error in your problem numbers 

If you want to dazzle the mind of whomever gave you this problem, 
tell them -40 is the correct answer, and it means the trip distance must 
be shortened by 40km for the given speed rates to work. 
If the distance becomes 260-40=220km, then the equations become 
x/80+(220-x)/100=2.5 
5x/400+4(220-x)/400=2.5 
5x+4(220-x)=2.5(400) 
5x+880-4x=1000 
x=120 
If x=120, then 220-x=100 
120/80=1.5 hrs and 100/100=1hr. 
Total=2.5 hours

anonymous · Answer

It would be no solution.