Speed/dist./time problem (need to find average speed)

[bigmac]

Homework Statement

Andrew won a two day bicycle race. He traveled 60km each day and his average speed on the second day was double that of the first day. If Andrew rode for a total of 6 hours, what was his average speed each day?

a) state an equation that models this problem.
b) Solve the problem.

Homework Equations

Speed = distance / time

The Attempt at a Solution

I tried to do it using the chart method but its not working out...I get x = 0.0333 km/h...the speed can't be that slow :S.

 

[thebigstar25]

(60/x) + (60/2x) = 6 >> (120/2x) + (60/2x) = 6 >> 180/2x = 6

>> 180 = 12 x , finally x =180/12 = 15 km/h .. what about this one :)

 

[bigmac]

yeah that works but, how did you take 2x as the LCD? don't you just multiply the denominators to get the LCD? And when you take 2x as a LCD, you cross multiply the left side right? I get 120x + 60x / 2x = 6...how did you get 120/2x + 60/2x...

 

[thebigstar25]

hmm, in the equation you have x and 2x in the denominators and you want to add them, in order to proceed the denominatos should be the same, and the shortest way to get them equal is by multiplying with 2 ( in the x denominator) ..

if it is still not clear please ask again, it is important that you be able to grasp this one..

 

[thebigstar25]

yeah that works but, how did you take 2x as the LCD? don't you just multiply the denominators to get the LCD? And when you take 2x as a LCD, you cross multiply the left side right? I get 120x + 60x / 2x = 6...how did you get 120/2x + 60/2x...

it seems that confuses you .. another way to solve it by taking 1/x as a common factor :

(60/x) + (60/2x) = 6 >> 1/x (60 + 60/2) = 6 >> 1/x (60 +30) = 6 >> 1/x (90) = 6

>> 1/x = 6/90 >> x = 90/6 = 15 km/h .. how about this one?