Answer:
Maria drove for 3.5 hours.
Step-by-step explanation:
Given :
Carlos and Maria drove a total of 258 miles in 5 hours.
Carlos drove the first part of the trip and averaged 53 miles per hour.
Maria drove the remainder of the trip and averaged 51 miles per hour.
To Find : For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.
Solution:
Carlos and Maria drove a total of 258 miles in 5 hours.
Let t be the time for which Carlos drove
So, Maria drove for hours = 5 - t
Speed of Carlos = 53 miles / hr
Distance covered by Carlos = [tex]Speed \times time [/tex]
= [tex]53t[/tex]
Speed of Maria = 51 miles per hour.
Distance covered by Maria = [tex]51 \times (5-t) [/tex]
Total Distance = [tex]53t+51 \times (5-t) [/tex]
Since we are given that Carlos and Maria drove a total of 258 miles
So, [tex]53t+51 \times (5-t)=258[/tex]
[tex]53t+255-51t=258[/tex]
[tex]2t+255=258[/tex]
[tex]2t=258-255[/tex]
[tex]2t=3[/tex]
[tex]t=\frac{3}{2}=1.5[/tex]
Carlos drove for 1.5 hours
Maria drove for hours = 5 - t = 5-1.5 =3.5 hours
Hence Maria drove for 3.5 hours.