9514 1404 393
Answer:
128 miles
Step-by-step explanation:
The convict has a head start of ...
distance = speed × time
distance = (8 mi/h) × (14 h) = 112 mi
That distance is being closed at a rate that is the difference between the speeds, so ...
64 mi/h -8 mi/h = 56 mi/h
The time it takes the guards to catch the convict will be ...
time = distance/speed
time = (112 mi)/(56 mi/h) = 2 h
The guards and prisoner will be at a distance from the prison of ...
distance = speed × time
distance = (64 mi/h)(2 h) = 128 mi
The convict will be caught 128 miles from the prison.
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<em>Check</em>
The convict will run an additional (8 mi/h)(2 h) = 16 mi after the guards start pursuit. That, in addition to the 112 miles already run, will total 112+16=128 miles, the same distance the guards travel in that 2 hours.
If the perimeter equals 30 and the length is twice the width, then the length is equal to 20 and the width is equal to 10.
Answer: 31 hope this helped
Step-by-step explanation: I'm assuming your problem looks like this: 4+5*6-3 =? To solve this problem you need to use the order of operations. PEMDAS which stands for Parentheses, exponents, multiply and divide, and lastly add and subtract. You must multiply and divide before you add and subtract so you must do 5*6 first. You now get 4+30-3. Now all you have left is addition and subtraction so you now just go from right to left and do one at a time. So 4+30 = 34 , 34-3=31. Therefore your answer should be 31. Hope that helped!
Answer:
Her speed on the summit was 35 mph.
Step-by-step explanation:
Her speed on the summit was "x" mph while her speed while climbing was "x - 10" mph. The distance she rode uphill was 55 miles and on the summit it was 28 miles. The total time she explored the mountain was 3 hours. Therefore:
time uphill = distance uphill / speed uphill = 55 / (x - 10)
time summit = distance summit / speed summit = 28 / x
total time = time uphill + time summit
3 = [55 / (x - 10)] + 28 / x
3 = [55*x + 28*(x - 10)]/[x*(x - 10)]
3*x*(x - 10) = 55*x + 28*x - 280
3x² - 30*x = 83*x - 280
3x² - 113*x + 280 = 0
x1 = {-(-113) + sqrt[(-113)² - 4*(3)*(280)]}/(2*3) = 35 mph
x2 = {-(-113) - sqrt[(-113)² - 4*(3)*(280)]}/(2*3) = 2.67 mph
Since her speed on the uphill couldn't be negative the speed on the summit can only be 35 mph.
