question:
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?
Responses
* college algebra word problem - Reiny, Tuesday, February 17, 2009 at 9:09am
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
* college algebra word problem - john, Tuesday, February 17, 2009 at 4:04pm
But wouldnt that actually factor into
(x-10)(x+45)
which would imply that the positive value for x is actually 10.
plugging that back into the problem, that means she can go 30 miles at 10 miles per hour and 20 miles at 25 miles per hour to arrive at 50 miles in an hour?
how can she go 30 miles at 10 miles per hour? the speed doesnt seem correct here.
* college algebra word problem....help - john, Tuesday, February 17, 2009 at 4:28pm
Is it possible that the equation should have been set up as:
30miles(xmiles/per 1 hour) + 20miles (x+15/per 1 hour) = ?
Im stuck
What were out of pocket expenses for elderly person in poor health when in a certain year his out of pocket expenses were $3335. More than someone in good health whose out of pocket expenses were $6667.
To solve this problem, we can use the equation:
30/x + 20/(x+15) = 1
where x represents the speed for the first leg of the trip.
To solve this equation, follow these steps:
Step 1: Multiply both sides of the equation by x(x+15) to eliminate the denominators:
30(x+15) + 20x = x(x+15)
Step 2: Expand and simplify the equation:
30x + 450 + 20x = x^2 + 15x
50x + 450 = x^2 + 15x
Step 3: Rearrange the equation to bring all terms to one side and set it equal to zero:
x^2 + 15x - 50x - 450 = 0
x^2 - 35x - 450 = 0
Step 4: Factor the quadratic equation:
(x+10)(x-45) = 0
This gives us two possible solutions: x = -10 or x = 45.
Since velocity cannot be negative in this context, we discard the -10 solution and conclude that the speed for the first 30 miles was 45 miles per hour.