SOLUTION: a family leaves home at 1pm, when billy asks are we there yet at 2:30pm they are 70 miles from gramdma's house, when jane asks at 2:45pm they are 55 miles away. how far from gra

Algebra ->  Linear-equations -> SOLUTION: a family leaves home at 1pm, when billy asks are we there yet at 2:30pm they are 70 miles from gramdma's house, when jane asks at 2:45pm they are 55 miles away. how far from gra      Log On


   

Question 1011261: a family leaves home at 1pm, when billy asks are we there yet at 2:30pm they are 70 miles from gramdma's house, when jane asks at 2:45pm they are 55 miles away.
how far from grandma's does the family live
at what time will the family arrive at grandma's
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Do we have to write linear equations?

WITH LINEAR EQUATIONS:
x= the family's speed (which for the purpose of this problem is constant), in miles per hour, and
y= total distance the family travels to grandma's house, in miles.
When Billy asks "Are we there yet?",
the family has been traveling for 1.5hours (from 1:00pm to 2:30pm).
They have traveled 1.5x miles, and their distance (in miles) to grandma's house is
y-1.5x=70 .
When Jane asks "Are we there yet?",
the family has been traveling for 1.75hours (from 1:00pm to 2:45pm).
They have traveled 1.75x miles, and their distance (in miles) to grandma's house is
y-1.75x=55 .
We need to solve the system
system%28y-1.5x=70%2Cy-1.75x=55%29-->system%28y-1.5x=70%2Cy-1.5x-%28y-1.75x%29=70-55%29-->system%28y-1.5x=70%2Cy-1.5x-y%2B1.75x%29=15%29-->system%28y-1.5x=70%2C0.25=15%29-->system%28y-1.5x=70%2Cx=15%2F0.25=60%29-->system%28y-1.5%2A60=70%2Cx=60%29-->system%28y-90=70%2Cx=60%29-->system%28y=70%2B90=highlight%28160%29%2Cx=60%29 .
So the family lives highlight%28160%29 miles from grandma's house,
and at 60 mph it would take them
160miles%2F%2260+mph%22=about2%262%2F3hours=2hours%2B40minutes ,
so they will arrive at grandma's house at 3%3A40pm .

THE FIFTH GRADER SOLUTION:
IN the 45-30=15 minutes between Billy's question and Jane's question
the family had traveled 70-55=15 miles,
so they are traveling 1 mile per minute.
When Billy asked, at 2:30pm, they were 70 miles from Grandma's house.
At 1 mile per minute, they will cover that distance in 70 minutes,
so they will arrive at grandma's house 70-minutes=1hour%2B10minutes after 2:30pm.
They will arrive at 2%3A30pm%2B1%3A10=3%3A40pm .