I don't really need the answer. I need help about word problems (The solution is what I need, and how you get it.). Here it is. A heavy freight train made a trip of 360 miles, running part of the distance at 54 miles an hour and the rest at 48 miles an hour. If the entire trip took 7 hours, find the distance traveled at each rate.
perhaps i can reframe my response to be more generally helpful for word problems.
what works for me for word problems:
what are the units given in the question?
mi / hr, hr, mi
what are the units of what the question wants?
distance - miles
what are the possible relevant formulas relating what you have and what you want?
speed = distance / time
how can i manipulate that formula to give me my end units?
distance = speed / time
so. we have two speeds.
we have total time.
to get to distance, we need to find how long we traveled at each of those speeds.
from these, we can start getting to he equations >>54448 posted.
[total_time] = [time_at_speed_a] + [time_at_speed_b]
speed * time = distance ... and we know the total distance
so... [speed_a] * [time_at_speed_a] + [speed_b] * [time_at_speed_b] = [total distance]
subbing in real values:
a + b = 7
54 * a + 48 * b = 360
and from here we have a normal system of linear equations to solve.
If I have difficulties with a problem I make some sketches and add the informations given one at a time.
total distance: 360 miles
total time: 7 hours
distance 1 ? distance 2 ?
velocity 1: 54 mi/h velocity 2: 48 mi/h
time 1 ? time 2 ?
It's then easy to see that the problem is composed of 2 pieces that needs to be calculated with the formula for constant velocity and that the sub solutions need to be added to obtain the total distance and total running time.