Math Problem

[calyxman]

Ran into this one in the lab and I'm trying to make sense of it (back of the book says the answer is 176 mph):

"In 1991 Rich Mears won the (500 mi) Indianapolis 500 race. His speed (rate) was 100 mph (the the nearest mph) faster than that of the 1911 winner, Ray Harroun. Mears completed the race in 3.74 hours less time than Harroun. Find Mears's rate to the nearest whole number."

Here's how I set it up initially:

D / r = t
500 / (x + 100) = t

Harroun's time can be expressed as 500 / x = t
Mears's time can then be expressed as 500 / x - 3.74 hours

So here's the final setup I had:

500 / (x + 100) = (500 / x) - 3.74

Am I going the right route?

 

[Hansr]

Yes, you should get x1=75.9722 and x2=-175.9722 and since you can't get negative mph since he isn't moving backwards in time you get his speed rounded up as 176 mph

 

[Jasonbot]

I made a table d=s.t (distance =speed.time)

d is constant (500)
speed: Mears=100+s
speed: Harroun=s
time: Mears=t-3.74
time: Harroun=t

then you do a simaltaneous equation

Harroun:
500=s.t
t=500-s

d=s.t
500=(100+s)[(500-t)-3.74]

Well, thats how I would do it. It's easier to do things without fractions IMO.

 

[calyxman]

Whoops, now I see my mistake. I forgot a zero when I was distributing the 500 with (x + 100). Careless mistake on my part.