Amotorcyclist travelling at a constant speed covered the distance between point m and point n in 5 hours. on the return trip, the first 36 km were traveled at that same speed. for the rest of the trip, the motorcyclist increased the speed by 3 km/hour. what was the motorcyclist’s original speed if the return trip took him 15 minutes less than the trip from m to n?

48 km/h

Step-by-step explanation:

Given in the question,

time taken by motorcyclist of he travel at constant speed = 5 hours

time taken by motorcyclist in the return trip = (5x60) - 15

                                                                        = 285 minutes

                                                                        = 4.75 hours

Suppose original speed = x km/h

                increased speed = (3+x) km/h

distance = time x speed

   y           = 5(x)

time = distance / speed

4.75 = 36/x + (y-36)/(x+3)

4.75 = 36/x + (5x-36) / (x+3)

4.75x(x+3) = 36(x+3) +  (5x-36)x  

4.75x² + 14.25x = 36x + 108 + 5x² - 36x

rearrange the terms

4.75x² -5x² + 14.25x = 108

-0.25x² + 14.25x - 108 = 0

by using quadratic equation

x = 48

x = 9

original speed of motorcyclist is x km/h that is 48 km/h

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.