One car went 10 miles farther when traveling at 50 mph than a second car that traveled 2 hours longer at a speed of 40 mph. How long did the first car travel?
time for first car --- t hours
time for 2nd car ------ t+2 hrs
distance covered by first car = 55t miles
distance covered by 2nd car = 40(t+2)
50t - 40(t+2) = 10
50t - 40t - 80 = 10
10t = 90
t = 9
the first car went for 9 hrs,
and the second went 11 hrs.
check:
distance covered by 1st car
= 9(50) = 450 miles
distance covered by 2nd car
= 11(40) = 440 miles
did the first go 10 miles farther?
YES
my answer is correct
To solve this problem, we can use the formula: distance = speed × time.
Let's assume the time the first car traveled is t hours.
The second car traveled for 2 more hours than the first car, so its time is t + 2 hours.
The distance traveled by the first car is calculated as:
distance1 = speed1 × time1 = 50 × t = 50t miles.
The distance traveled by the second car is calculated as:
distance2 = speed2 × time2 = 40 × (t + 2) = 40t + 80 miles.
Given that the first car traveled 10 miles farther than the second car, we can set up the equation:
50t = 40t + 80 + 10
Simplifying the equation, we get:
10t = 90
Dividing both sides of the equation by 10, we find:
t = 9
Therefore, the first car traveled for 9 hours.
To solve this problem, let's break it down step by step:
Step 1: Identify the given information.
We are given two speeds: 50 mph for the first car and 40 mph for the second car. We are also given that the second car traveled for 2 hours longer than the first car. Lastly, we know that the first car went 10 miles farther than the second car.
Step 2: Convert the units for consistent calculations.
Since we are given speeds in miles per hour (mph), it's important to make sure we have consistent units for the distance. We can keep the distance in miles, which matches the given speeds.
Step 3: Setup equations.
Let's denote the time traveled by the first car as 't1' and the time traveled by the second car as 't2'. We can write the following equations based on the given information:
Distance traveled by the first car (d1) = Speed of the first car (s1) multiplied by the time traveled by the first car (t1).
Distance traveled by the second car (d2) = Speed of the second car (s2) multiplied by the time traveled by the second car (t2).
From the given information, we can also write the equation:
d1 = d2 + 10.
Step 4: Express time in terms of the other variables.
Since we are given that the second car traveled 2 hours longer than the first car, we can express 't2' in terms of 't1' as follows: t2 = t1 + 2.
Step 5: Substitute the expressions.
Substituting the expressions from Step 4 into the equations from Step 3, we get:
s1 * t1 = s2 * (t1 + 2) + 10.
Step 6: Solve the equation.
Now, let's solve the equation to find the value of 't1', which represents the time traveled by the first car:
50t1 = 40(t1 + 2) + 10.
Expanding the right side of the equation, we get:
50t1 = 40t1 + 80 + 10.
Combining like terms, we have:
50t1 = 40t1 + 90.
Subtracting 40t1 from both sides, we get:
10t1 = 90.
Dividing both sides by 10, we find:
t1 = 9.
Therefore, the first car traveled for 9 hours.