You travel 800 miles in 10 hours. Some of the trip you drive 75 mph and some you drive 90 mph. How long did you drive (and how many miles) for each of the two speeds?

Answer 1

First let's develop equations from the problem given

***NOTE, since MPH is in Miles and Hours, and the given information is in Miles and Hours, no Unit conversion is needed. Thus, I won't put in the units below***

let the following be givens :

t₇₅ = time at 75 mph in hours

t₉₀ = time at 90 mph in hours

Equation 1 : ( 75 * t₇₅ ) + ( 90 * t₉₀ ) = 800

Equation 2 : t₇₅ + t₉₀ = 10

Use Equation to solve for t₇₅

t₇₅ + t₉₀ = 10

subtract t₉₀ from both sides

t₇₅ = 10 - t₉₀

Plug that value of t₇₅ into Equation 1 to solve for t₉₀

( 75 * (10 - t₉₀) ) + ( 90 * t₉₀ ) = 800

750 - 75*t₉₀ + 90*t₉₀ = 800

combine like terms

750 + 15*t₉₀ = 800

subtract 750 from both sides

15*t₉₀ = 50

divide both sides by 15

t₉₀ = 3.3333 hours (10/3 to be exact)

plug that into Equation 2 to solve for t₇₅

t₇₅ + t₉₀ = 10

t₇₅ + 3.333 = 10

subtract 3.333 from both sides

t₇₅ = 6.666 hours (20/3 to be exact)

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Always check your work!

( 75 * t₇₅ ) + ( 90 * t₉₀ ) = 800

( 75 * (20/3) ) + ( 90 * (10/3) ) = 800

CORRECT!!

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How many miles doing 75 & 90 mph?

distance₇₅ = 75 * (20/3) = 500 miles

distance₉₀ = 90 * (10/3) = 300 miles

I hope this helps you.