Respuesta :
Answer:
Slower speed = 70 mph
Faster speed = 100 mph
Explanation:
Let the slower speed be x miles per hour
Then, the faster speed = (x+30) miles per hour
Let the time spent driving at the slower speed (that is, at x mph) = t
Then, time spent driving at the faster speed (that is, at (x+30) mph) = 2t
speed = (distance)/(time)
Distance = speed × time
Distance covered during the slower speed = x × t = xt = 70 (given in the question)
xt = 70 (eqn 1)
At the faster speed
Distance covered = (x+30)(2t) = 2t(x+30)
Distance covered during faster speed = 200 miles
2t(x+30) = 200
2xt + 60t = 200
Recall (eqn 1)
xt = 70
2(70) + 60t = 200
60t = 60
t = 1 hour.
xt = 70
Slower speed = x = 70 mph
Faster speed = (x+30) = 100 mph
complete question:
A driver of a car took a day trip around the coastline driving at two different speeds. He drove 70 miles at a slower speed and 200 miles at a speed 30 miles per hour faster. If the time spent driving at the faster speed was twice that spent driving at the slower speed, find the two speeds during the trip.
Answer:
slower speed
speed = 70 miles/hr
Faster speed
speed = 100 miles/hr
Explanation:
The driver took a day trip at two different speed. The first speed was slower while the second was faster.
let the speed be divided into 2
Slower speed
speed = a
distance = 70
speed = distance/time
time = distance/speed
time = 70/a
Faster speed
speed = a + 30
distance = 200
speed = distance/time
time = distance/speed
time = 200/a + 30
Since the faster speed time is twice the slower speed time it can be represented as follows:
2 × 70/a = 200/a + 30
140/a = 200/ a + 30
cross multiply
140a + 140(30) = 200a
4200 = 200a - 140a
4200 = 60a
divide both sides by 60
4200/60 = a
a = 70
Inserting the value of a in the time of the faster speed formula
time = 200/a + 30
time = 200/100
time = 2 hr
slower speed
speed = distance/time
speed = 70/1
speed = 70 miles/hr
Faster speed
speed = distance/time
speed = 200/2
speed = 100 miles/hr
