Respuesta :
Answer:
380
Step-by-step explanation:
This is a bit nasty. It depends on how you read the 20 miles more and what you do with it. The best and most careful way to do it is do it a long way setting up the two equations carefully.
Second day
Let the time travelled = t
Let the speed travelled = 60 mph
d2 = 60*t
First Day
40*(t + 2) = d1
but d1 = d2 + 20 because he travelled 20 miles further on d1
40 * (t + 2) = d2 + 20
d2 however = 60*t
40*(t+2 ) = 60*t + 20 Remove the brackets
40t + 80 = 60t + 20 Subtract 20 from both sides
40t + 60 = 60t Subtract 40t from both sides
60 = 20*t Divide by 20
t = 60/20
t = 3 hours.
Day 2 = 60 + t = 180
Day 1 = 40*5 = 200
Total distance = 380
Where did that 20 miles go? It was just an observation about the difference in distance travelled between the 2 days.
The total distance the driver traveled in the two days is 260 miles
From the question, on the first day, the driver was going as a speed of 40 mph.
Let s be speed
∴ [tex]s_{1}= 40mph[/tex]
On the second day, he increased the speed to 60 mph
∴ [tex]s_{2}= 60mph[/tex]
From the statement- If he drove 2 more hours on the first day
Let time be t
Then
[tex]t_{1}= t_{2} + 2[/tex] hrs
and traveled 20 more miles
Let d be distance
Then,
[tex]d_{1}= d_{2} + 20[/tex] miles
From the formula
Distance = Speed × Time
Then,
[tex]d = s \times t[/tex]
∴ [tex]d_{1} = s_{1} \times t_{1}[/tex]
From above,
[tex]d_{1}= d_{2}+20[/tex] miles
[tex]s_{1}= 40mph[/tex]
[tex]t_{1}= t_{2} + 2[/tex] hrs
Putting these into
[tex]d_{1} = s_{1} \times t_{1}[/tex]
[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex] ...... (1)
But,
[tex]Time = \frac{Distance}{Speed}[/tex]
∴ [tex]t_{2}= \frac{d_{2} }{s_{2} }[/tex]
From above, [tex]s_{2}= 60mph[/tex]
∴ [tex]t_{2}= \frac{d_{2} }{60}[/tex]
Put this into equation (1)
[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex]
[tex]d_{2} + 20 = 40\times (\frac{d_{2}}{60} +2)[/tex]
[tex]d_{2} + 20 = \frac{2}{3}d_{2} +80\\d_{2} = \frac{2}{3}d_{2} +80-20\\d_{2} = \frac{2}{3}d_{2} +60[/tex]
Multiply through by 3
[tex]3\times d_{2} = 3\times \frac{2}{3}d_{2} +3 \times 60\\3d_{2} = 2d_{2} + 120\\3d_{2} -2d_{2} = 120[/tex]
∴ [tex]d_{2} = 120[/tex] miles
∴The distance traveled on the second day is 120 miles
For the distance traveled on the first day,
Substitute [tex]d_{2}[/tex] into the equation
[tex]d_{1}= d_{2}+20[/tex] miles
∴ [tex]d_{1}= 120+20[/tex]
[tex]d_{1}= 140[/tex] miles
∴ The distance traveled on the first day is 140 miles
The total distance traveled in the two days = [tex]d_{1} + d_{2}[/tex]
The total distance traveled in the two days = 120 miles + 140 miles
The total distance traveled in the two days = 260 miles
Hence, the total distance the driver traveled in the two days is 260 miles
Learn more here: https://brainly.com/question/23531710
