rachel allows herself 1 hour to reach a sales appt 50 miles away. after she has driven 30 miles, she realizes that she must increase her speed by 15mph in order to get there on time. what was her speed for the first 30 miles?
If you had worked out my solution from several pages back
http://www.jiskha.com/display.cgi?id=1234871808
you would have realized that it was a simple typo, but my factors and my solution was correct.
I will repeat the corrected version
let her speed for the first leg be x mph
let her speed for the second leg be x+15 mph
so her time for the first leg is 30/x
her time for the second leg is 20/(x+15)
but 30/x + 20/(x+15) = 1
multiplying both sides by x(x+15) and simplifying I got
x^2 + 35x - 450 = 0
(x+10)(x-45) = 0
x = -10, which is silly or
x = 45 mph
check:
30/45 + 20/60 = 1
oops, copied it and forgot to change the typo, silly me.
let her speed for the first leg be x mph
let her speed for the second leg be x+15 mph
so her time for the first leg is 30/x
her time for the second leg is 20/(x+15)
but 30/x + 20/(x+15) = 1
multiplying both sides by x(x+15) and simplifying I got
x^2 - 35x - 450 = 0
(x+10)(x-45) = 0
x = -10, which is silly or
x = 45 mph
thank you so much, I really appreciate your time.
To find Rachel's speed for the first 30 miles, we can use the concept of average speed.
Let's break down the information given:
Distance to travel = 50 miles
Time given = 1 hour
Since Rachel realizes that she must increase her speed, we can assume that the speed for the first 30 miles is different from the speed for the remaining 20 miles.
Let's first calculate the time it would take for her to travel the remaining 20 miles:
Distance remaining = 50 miles - 30 miles = 20 miles
To travel the remaining 20 miles, she has 1 hour - (time taken for the first 30 miles).
Now, let's calculate the time taken for the remaining 20 miles:
Time = 1 hour - (time taken for the first 30 miles)
Next, we'll find the speed required for the remaining 20 miles by using the formula:
Speed = Distance / Time
Substituting the values, we get:
Speed = 20 miles / (1 hour - time taken for the first 30 miles)
Finally, since Rachel must increase her speed by 15 mph, we can set up the equation:
Speed for the first 30 miles + 15 mph = Speed for the remaining 20 miles
Now, let's solve the equation to find Rachel's speed for the first 30 miles:
Speed for the first 30 miles + 15 mph = 20 miles / (1 hour - time taken for the first 30 miles)
Now, we have an equation with only one variable, which we can solve to find Rachel's speed for the first 30 miles.