Question

Lexi runs a race at school. She runs at a rate of 4 miles per hour for the first mile, then increases her rate to 5 miles per hour until the last mile when she runs 6 miles per hour. Which equation below represents her time, T. In hours, If she runs a total of x miles

Answer 1

Answer:

60T = 12x - 1

Step-by-step explanation:

In speed distance and time, time(t) is given by

time = distance(d)/speed(s)

total distance ran = x miles

case 1

d = 1 mile

speed = 4 miles per hour

as time = distance(d)/speed(s)

t = 1/4

____________________________

case 2

speed = 5 miles per hour

it is given that out of x miles for first mile and last mile her speed was 5 miles per hour

thus distance for this speed can be calculated by

subtracting first and last mile from x miles

therefore

distance = x-2 miles\

t = (x-2)/5

_____________________________________

case 3

distance = 1 mile

speed = 6 miles per hour

t = 1/6

______________________________

Total time T as required  will be sum of time for the 3 case calculated above

T = 1/4 + (x-2)/5 + 1/6

T = 1/4 + (x - 2)/5 + 1/6   (taking LCM of 6,5,4 as 60 and solving)

T = (15 + 12x - 24 + 10)/60

T = (12x - 1)/60

60T = 12x - 1

Thus, equation 60T = 12x - 1 represents her time T