Question

I was wondering if somebody would be willing to help clear-up my misunderstanding of this problem?

One speed skater starts across a frozen lake at an average speed of 8 meters per second. Ten seconds later, a second speed skater starts from the same point and skates in the same direction at an average speed of 10 meters per second. How many seconds after the second skater starts will the second skater overtake the first skater?

I attempted to the problem as follows:

8t = 10(t-10)
t = -50
This is not the correct solution. I was able to to find the very same question online, solved p

Answer 1

you start with
8t= 10(t-10)
distribute the 10
8t= 10t -100
what is a good next step ?

Answer 2

Solve the equation for t and you get -50; right?

Answer 3

Or 50 I should say.

Answer 4

you know the answer is not negative. You should show your next step, so we can figure out the "bug" in your algebra

Answer 5

8t = 10t + 100
8t - 10t = 100
-2t = 100
t = -50
I understand that shouldn't have a negative time but I've rearranged this equation every way I can think of and I can't get 40.

Answer 6

Your very first equation looks wrong.
we start with
8t= 10(t-10)
distribute the 10
8t= 10t -100

now try again

Answer 7

8t - 10t = -100
-2t = -100
t = 50 right???

Answer 8

the slow skater goes for 50 seconds
the faster skater goes for (t-10) or 40 seconds

Answer 9

Grrr!!!! I'm never going to understand how to solve word problems :(.

Answer 10

Thank you very much my friend! Have a good day.

Answer 11

because the question is
How many seconds after the second skater starts will the second skater overtake the first skater?

is asking about the fast skater, you could have said: let t be the time of the fast skater
the slow skater will take 10 seconds longer, or t+10
they meet when both have gone the same distance.
distance is rate * time so we can say
8 (t+10)= 10 t
solve for t (of the fast skater): 8t+80= 10t
2t=80
t= 40 seconds