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
