Speed on a Car Trip

Question

During the first part of a trip, Tara's honda traveled 120mi at a certain speed. Tara then drove another 100mi at a speed that was 10mph slower. If the total time of Tara's trip was 4hr, what was her speed on each part of the trip?

Answer 1

1st trip with 120 miles at v speed

2nd trip with 100 miles at v-10 speed

Total time or t is 4 hours

 

Distance equation is d = vt

Or t = d/v

In this case,

t = d1/v + d2/(v-10)

4 = (120/v) + (100/(v-10))

Divide 4 on both sides to get:

1 = (30/v) + (25/(v-10))

Add these two fractions with common denominator v(v-10)

(30(v-10)+25v)/(v(v-10)) = 1

Multiply v(v-10) on both sides and distribute all the terms to get

30v-300+25v=v²-10v

v²-10v-30v-25v+300=0

v²-65v+300=0

Solve for v using quadratic equation:

v=(65±sqrt((-65^2)-(4*1*300)))/2

v=(65±55)/2

v={60,5}

 

Lets try both values of speed or v we got what is given to us for speeds:

If v = 60mph

Then speed during first trip is 60mph and speed during second trip is 60-10=50 mph

 

If v=5mph

Then speed during first trip is 5mph and speed during second trip is 5-10=-5mph (a negative speed). A negative speed is not feasible since 2nd trip is supposed to have 10mph less speed than first and its not realistic.

 

Therefore, 60mph is the speed during 1st trip and 50 mph is the speed during 2nd trip.