Using the formula d=r*thow would you solve this using the system of linear equations?

Ella spent 4.5 hours on her bicycle.

Step-by-step explanation:

Let b represent the time Ella spent riding. Then the distance in miles she rode on the bicycle at 24 miles per hour is ...

... d = r·t = 24b

The time she spent walking is b hours less than the 6 hours of her total trip time, (6-b). The distance in miles she walked at 4 miles per hour is ...

... d = r·t = 4(6-b)

The total of these two distances is 114 miles.

... 24b +4(6 -b) = 114

... 24b +24 -4b = 114 . . . . . eliminate parentheses

... 20b = 90 . . . . . . . . . . . . subtract 24

... b = 90/20 = 4.5 . . . . . . divide by the coefficient of  b

Ella spent 4.5 hours riding.

System of equations

In the above, we have written one equation in one unknown, the value the problem asks for. We could use another variable to represent the time Ella spent walking. Call that w. Then our system of equations is ...

... b + w = 6 . . . . . total time spent riding and walking is 6 hours

... 24b +4w = 114 . . . . total distance traveled is r·t at each speed, added together

If we solve the first equation for w, we get w = 6-b. If we substitute that into the second equation, we get

... 24b +4(6-b) = 114 . . . . . this should look familiar. It is the equation we wrote above.

The solution is (b, w) = (4.5, 1.5).

step-by-step explanation: