Sarah drove 3 hours more than Michael on their trip to Texas. If the trip took 37 hours, how long did Sarah and Michael each drive?Can you please translate the word problem into an algebraic...

Sarah drove 3 hours more than Michael on their trip to Texas. If the trip took 37 hours, how long did Sarah and Michael each drive?

Can you please translate the word problem into an algebraic expression using x as the unknown.Then solve for x.

Asked on by melmel654

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Top Answer

kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

Let x be the number of hours that Michael took the wheel. Then x + 3 (three hours more) is the time that Sarah drove. The total time for the trip is the number of hours that Michael drove plus the number of hours that Sarah drove.

So x + x + 3 hours = 37 hours, or:

2x + 3 = 37

2x = 34

x = 17 hours

 

So Michael drove for 17 hours and Sarah for 20 hours.

eblount's profile pic

eblount | High School Teacher | (Level 1) Adjunct Educator

Posted on

Let x = Michael's hours

Let x + 3 = Sarah's hours

The equation will equal 37, the total amount of hours.

x + x + 3 = 37

2x + 3 = 37

2x + 3 -3 = 37 -3

  2x = 34

2x/2x = 34/2

   x = 17

Michael hours = 17

x + 3 or 17 + 3 = 20

Sarah's hours = 20

Top Answer

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

Solution witout Algebra:

If the extra 3 hours are separated from 37 hours of the trip, we get34 hours which is driven equally by Sarah and Michael. So, 34/2=17 hours are equally driven by both out of 34 hours. Now add Sarah's part of extra 3 hours. So, Sarah drove 17+3 =20 Hours, and Michel drove 17 hours.

Method of Agebra:

The driving  hours by Sarah is known in terms of driving of Michale plus 3 hours.. So, the unknown hours of driving of Michale is assumed to be x hrs which is the basic unknown to solve in this word problem. Then Sarah's duration of driving is x+3 hours. So, their total hours of driving (algebaically)=x+x+3=2x+3 hours. Butsthis is equal to 37 hours. The basic requirement of the word problem is to set up an equation. So,the equation of this word  problem is:

2x+3=37

where x is the basic unknown hours of Michale's driving hours. Once you solve for x, you get x+3 as duration in hours of Sarah's driving.

Solving the equation:

2x+3=37

Subtract 3 from both sides:

2x+3-3=37-3

2x=34

Divide both sides by 2

2x/2=34/2

x=17 hours, is the duration of Michel's drive and

x+3=17+3=20 hours is that of Sarah's.

 

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

Sarah drove 3 hours more than Michael on their trip to Texas. If the trip took 37 hours, how long did Sarah and Michael each drive?

In order to solve this algebraically let us assume that x is the unknown variable, since Sarah drove 3 hours more than Michael than we can say that she drove x+3 hours whereas Michael drove x hours. The total number of hours is 37.  

Therefore, (x+3)+x=37

                x+3+x=37

                2x+3=37

                2x=37-3

                2x=34

                  x=34/2

                  x=17   

Therefore Michael drove 17 hours and Sarah drove 17+3 hours i.e 20 hours. 

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