Concept explainers
To calculate the number of hours Bruins basketball team spent driving on local highways.
Bruins basketball team spent 4.5 hours of driving on local highways.
Given:
Total distance of trip = 560 miles
Speed on local highways = 45 mph
Speed on interstate highways = 55 mph
Number of hours spent more on the interstate highways than local highways = 2 hours
Formula used: Average speed of the team is determined by calculating the ratio of distance travelled to time taken to cover this distance, i.e.
Speed (v)=Distance (d)Time (t)
Calculation:
Let the time spent on local highways = tl
Let the time spent on interstate highways = ti
Let the average speed on local highways = vl
Let the average speed on interstate highways = vi
Let total distance = dt
Let the distance of local highways = dl
Let the distance of interstate highways = di
Now, from the given information, we have:
ti=tl+2vl=45 mphvi=55 mphdt=560 miles
Now, the average speed on local highways is given by:
vl=dltl45=dltl ⋯(1)
And, the total distance travelled is given by:
dl+di=560 ⋯(2)
And, the average speed on interstate highways is given by:
vi=diti55=560−dltl+2 ⋯(3)
From equation (1), we have:
dl=45tl
Substituting the value of dl in equation (3) , we have:
55=560−45tltl+2⇒55tl+110=560−45tl⇒55tl+45tl=560−110⇒100tl=450⇒tl=450100⇒tl=4.5 hours
Hence, Bruins basketball team spent 4.5 hours of driving on local highways.
Chapter 1 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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