distance problem
suzi drove home at 60mph,but her brother jim,who left at the same time, could drive at only 48mph. When suzie arrived, jim still had 60 miles to go. How far did suzi drive?
They separated at a rate of 12 mph. It took 5 hours for the distance between them to become 60 miles. Suzy drove 60 x 5 = 300 miles in that time
To solve this distance problem, we can use the formula:
Distance = Speed x Time
Let's assume the time it took Suzi to drive home as 't' hours.
We know Suzi's speed is 60 mph, so her distance can be calculated as:
Suzi's Distance = 60 mph x t
Now, considering Jim's speed is 48 mph and he still had 60 miles to go when Suzi arrived, we can calculate his distance as:
Jim's Distance = 48 mph x (t + x)
Here, 'x' represents the extra time Jim needed to finish his journey.
Since Suzi arrived when Jim had 60 miles remaining, we can write an equation using the distances:
Suzi's Distance = Jim's Distance + Remaining Distance
60 mph x t = 48 mph x (t + x) + 60 miles
Simplifying this equation:
60t = 48t + 48x + 60
Now, we can solve this equation to find the value of 't', which represents the time Suzi drove. Let's calculate it:
60t - 48t = 48x + 60
12t = 48x + 60
12t - 48x = 60
Dividing both sides by 12:
t - 4x = 5
We have the equation t - 4x = 5. But we don't know the value of 'x' yet. To find it, let's use the information that Jim still had 60 miles to go when Suzi arrived.
Using the formula for Jim's distance:
Jim's Distance = 48 mph x (t + x)
Plugging in the given information:
Jim's Distance = 48 mph x (t + x) = 60 miles
Simplifying this equation:
48(t + x) = 60
48t + 48x = 60
Now, solve this equation for 'x':
48x = 60 - 48t
x = (60 - 48t) / 48
Substituting the value of 'x' back into the equation t - 4x = 5, we can solve it:
t - 4((60 - 48t) / 48) = 5
Now, let's solve this equation to find the value of 't':
t - (60 - 48t) / 12 = 5
12t - (60 - 48t) = 60
12t - 60 + 48t = 60
60t = 120
t = 120 / 60
t = 2
Therefore, Suzi drove for 2 hours.
Now, we can calculate the distance she traveled:
Suzi's Distance = 60 mph x t
Suzi's Distance = 60 mph x 2
Suzi's Distance = 120 miles
So, Suzi drove 120 miles.