SOLUTION: The distance (in miles) traveled when driving at a certain speed s for 38 hours, then driving 13 miles/hour faster for another hour. Express the distance in terms of s

Question 1014193: The distance (in miles) traveled when driving at a certain speed s for 38 hours, then driving 13 miles/hour faster for another hour. Express the distance in terms of s
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance

rate and speed mean the same thing in this type of problem.

therefore, rate * time = distance becomes s * time = distance.

the problem states that you are traveling at a speed of s miles per hour for 38 hours and then at a speed of 13 miles per hour faster than s for another hour.

if you let d1 = the distance at s miles per hour for 38 miles and d2 = the distance at s + 13 miles per hour for 1 hour, then you get d = d1 + d2.

this results in:

d = d1 + d2
d1 = 38s
d2 = 1*(s+13) = s+13
d = d1 + d2 = 38s + s + 13

combine like terms to get d = 39s + 13.

that's your solution.

confirm by assigning a random value of speed to replace.

i chose 40 miles per hour.

s = 40 miles per hour.
d = 39s + 13 becomes d = 39*40 + 13 which becomes d = 1573.

d also equals d1 + d2.
d1 = 38s
d2 = s + 13

when s = 40, this becomes:

d1 = 38 * 40 = 1520
d2 = 40 + 13 = 53
d1 + d2 = 1520 + 53 = 1573 = d

you get the same answer with both formulas, so the solution looks good.

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