I left Boston for Washington, DC, at 7:00 am. At first, my speed was 55 mph; then it was 75 mph. I traveled 630 miles in 10 hours. At what time did I begin to drive faster?

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)

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