Answer:
We began to drive at 75 mph at 1:00 p.m.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Speed at the beginning of the trip = 55 mph
Speed at the end of the trip = 75 mph
Distance from Boston to Washington D.C. = 630 miles
Time of the trip = 10 hours
2. At what time did I begin to drive faster?
Let's recall that Speed = Distance/Time, therefore Time = Distance/Speed
Let x represent the distance we drove at 55 mph and 630 - x the distance we drove at 75 mph, thus:
Time we drove at 55 mph + Time we drove at 75 mph = Time of the trip
Replacing with the real values, we have:
x/55 + (630 - x)/75 = 10
75x + 55 * (630 - x) = 41,250 (4,125 as Lowest common multiple)
75x + 34,650 - 55x = 41,250
20x = 41,250 - 34,650 (Subtracting 34,650 at both sides)
20x = 6,600
x = 6,600/20
x = 330 ⇒ 630 - x = 300
Time we drove at 55 mph = 330/55 = 6 hours
Time we drove at 75 mph = 300/75 = 4 hours
We began to drive at 75 mph at 1:00 p.m. (7 am + 6 hours)
