This is a
distance, time, speed problem using the equation
distance = speed * time or D = S * T
We have two unknowns, distance and time, but we have information to
relate the two. If we let Tm be the time it takes to get to the mountains and
Tb be the time to get back from the mountains then we can say that
EQ1: Tb = Tm + 1 (she took an extra hour to get home)
and if we let Dm be the distance to the mountains and Db the distance back from
the mountains we have
EQ2: Dm = Db + 10
(a route that was 10 miles shorter)
The only other
information we have are the speeds 55mph and 40mph and with these and
D = S * T, we can change EQ1 into EQ2 or vice versa to eliminate one of our
unknowns.
EQ2 becomes 55mph * Tm = 40mph * Tb + 10 miles (using D = S * T)
and using EQ1 we have
55mph * Tm = 40mph * (Tm + 1hr) + 10 miles (eliminate Tb)
55mph * Tm = 40mph * Tm + 40 mph * 1hr + 10 miles (now solve for Tm)
55mph * Tm = 40mph * Tm + 40 miles + 10 miles
55mph * Tm - 40mph * Tm = 50 miles
15mph * Tm = 50 miles
Tm = 50 miles / 15 mph
Tm = 10 miles / 3 mph = (10/3) hours = 3 hours and 20 mins.
substituting this into EQ1 we have
Tb = 4 hours and 20 minutes = 13/3 hours
now the total distance she travelled is Dm + Db and since we have both times
available and both speeds we have
Dm = 55mph * (10/3) hours = 183 1/3 miles (using D = S * T again)
Db = 40mph * (13/3) hours = 173 1/3 miles
Dm + Db = 356 2/3 miles.
So, the answer is
356 2/3 miles. (356.6 miles) Sometimes, making a table to organize the
information from the problem statement can help
|
Distance |
Speed |
Time |
| To |
Dm |
55 mph |
Tm |
| Back |
Db = Dm - 10 |
40 mph |
Tb = Tm + 1hr |