Word Problem: Distance=rate x time; does it have a solution?

[Algebra2Blues]

Freshman - Algebra 2. Post-summer block. Please help.

=\ I know, second problem in one day, but this one has me stumped:

John drove part of a 260km trip at 80 km/h and the rest at 100km/h.
Find the distance he travelled at 80 km/h if is total driving time was 2h and 30min.

I know this involves d=r x t.
But I feel as if I'm missing a vital part, as in it isn't said in the problem.
This problem is under a section that says "if there is not enough information to solve the problem or if it has no solution, say so."

Please and thank you.

 

[Deleted member 4993]

Re: Word Problem: Distance=rate x time; does it have a solut

Freshman - Algebra 2. Post-summer block. Please help.

=\ I know, second problem in one day, but this one has me stumped:

John drove part of a 260km trip at 80 km/h and the rest at 100km/h.
Find the distance he travelled at 80 km/h if is total driving time was 2h and 30min.

I know this involves d=r x t.
But I feel as if I'm missing a vital part, as in it isn't said in the problem.
This problem is under a section that says "if there is not enough information to solve the problem or if it has no solution, say so."

Please and thank you.

Suppose

distance traveled at 80 kmph = d km

distance traveled at 100 kmph = (260 - d) km

time traveled at 80 kmph = d/80 hrs

time traveled at 100 kmph = (260-d)/100 hrs

Above equation can be solved easily...

But this problem is strange

Think about it

How long would it take to finish the trip, if John drove at 100 kmph all the way (the whole 260 km)?

 

[Algebra2Blues]

It would take John 2.6 hours to complete it.

I got that far following what you posted previously, but I can't make sense of it after that; do I then substitute the d to solve for 80km/h?

EDIT: When I do the same steps for 80km/h, I end up with d/80 = d/80. The statement is true but it doesn't answer the question. How do I get to an answer there?

 

[skeeter]

John drove part of a 260km trip at 80 km/h and the rest at 100km/h.
Find the distance he travelled at 80 km/h if is total driving time was 2h and 30min.

check the problem statement again ... as posted, your problem has no possible solution.

 

[Denis]

It would take John 2.6 hours to complete it.

YES: 2.6 hours if he drove at 100 for the FULL distance;
BUT the time given is 2.5 hours; plus he drove part at 80:
isn't that enough for a "NO SOLUTION" :idea:

Btw, if you solve, there will be a theoretical solution:
d / 80 + (260 - d) / 100 = 2.5
Solve to get d = -40

So John "backed up" 40 miles (1/2 hour at 80), leaving 300 miles;
he then travelled that 300 miles at 100, so 3 hours,
but a net of 2.5 hours since he backed up for -1/2 hour :!: