help me with this one last on question so that i can get the hang of it?

Question

Jamie ran two laps around a track in 99 s. How long did it take him to run each lap if he ran the first lap at 8.5 m/s and the second at 8.0 m/s?

First lap: 45 s; second lap: 54 s

B.
First lap: 46 s; second lap: 53 s

C.
First lap: 47 s; second lap: 52 s

D.
First lap: 48 s; second lap: 51 s

Answer 1

Let's call the entire track length x, measured in meters.

To arrive at the time, we have to divide the distance by the speed:

x / 8.5 + x/8.0 = 99

multiply all sides by 8.5 and by 8.0

8.0 X + 8.5 X = 8.0 * 8.5 *99

16,5 X = 8*8.5*99

X = 8*8.5*99/16.5

Time for the first lap:
T1 = X / 8.5 s
T1 = 8*99/16.5 s

T2 = X / 8.0 S
T2 = 8.5*99/16.5 s


calculator time....

Solution D

Answer 2

Whenever you have problem with multiple rates, you have to right multiple equations:

T1 + T2 = T
D1 + D2 = D
R1*T1 = D1
R2*T2 = D2

Since you have total time (T), R1, and R2, you are left with variable T1, T2, D1, D2, and D. But D1 and D2 are equal (same track/distance both laps)! So you can then say

R1*T1 = R2*T2

Combine this with the first equation, and you have 2 equations and 2 unknowns, which is solvable using standard algebraic techniques (combination or substition).

The take-home message is this: any time you have these multiple-stage distance/time/rate problems, write out as many equations as you can, use facts of the situation to set things equal if possible (like we did here with the D1 & D2), and you will eventually end up with an equal number of equations and unknowns.

Answer 3

Okay, letting x be the distance around the track, then (x/8.5)+(x/8) = 99.
So, lets mutiply each side by (8*8.5), giving us 8x+8.5x=6732.
So, 16.5x=6732, or x=6732/16.5 =408.

So, he ran first lap in 408/8.5 = 48 sec, and 2nd in 408/8 = 51 sec.