Last question of the day, I promise! lol...
I am having a real hard time translating word problems having to do with distance and time. I dont understand the concept of it for some reason.. The problem I am trying to solve is this:
"On a 300 mile trip to Chicago, Josh drove part of the time at 60 mph and the remainder of the trip at 70 mph. If the total trip took 4.5 hours, for how many miles did Josh drive at a rate of 60 mph?"
Can someone teach me how you are supposed to set these problems up? My teacher gave us the equation 60x + 70(4.5 - x) = 300, but I dont understand how we get there.
why are we subtracting 4.5 (time) from the miles driven (x)? I dont get it...
At 60 mph for x hours, Josh drove 60x miles. At 70 mph for 4.5- x hours, Josh drove 70(4.5- x) miles. Putting those together, Josh drove 60x+ 70(4.5- x) miles and we are told that he drove 300 miles: 60x+ 70(4.5- x)= 300. Once you have solve for x in hours, multiply by 60 mph to find the number of miles he drove.
I strongly recommend that, for any problem like this, when you write out an equation, explicitely write out what any variables in that equation recommend. For this problem you should have written out clearly "x is the time, in hours, that Josh drove at 60 mph". That will help you keep track of what you are doing (and really shock your teacher).