Math, asked by maleikabarbado0825, 8 months ago

Can u help me solve these with solutions please?

1.) Terry, a marathon runner, ran from her house to the high school then back. The return trip took 5 minutes longer. If her speed was 10 mph to the high school and 9 mph to her house, how far is Terry's house from the high school?

2.) At 2:00 pm, a car leaves town A and another leaves town B. The distance between two towns is 60 km. One car travels 10 kph faster than the other. The car passes at each other at 2:30 pm. How far does each travel?

3.) An alloy which weighs 118 kilograms is 10% silver. How much silver must be added to produce a metal that is 25% silver?

4.) How much decaffeinated coffee (assume this means 0% caffeine) and 50% caffeine coffee should be mixed to produce 25 cups of 40% caffeine coffee?

Answers

Answered by amitnrw
0

Given : return trip took 5 minutes longer. If her speed was 10 mph to the high school and 9 mph to her house,

To find :  how far is Terry's house from the high school?

Solution:

Let say Terry's house from the high school = D  Miles

Time Taken in going School = D/10 hr =  60D/10  = 6D  Min

Time Taken returning from School = D/6 hr =  60D/9  = 20D/3  Min

20D/3 -  6D   = 5

=> 20D - 18D = 15

=> 2D = 15

=> D = 7.5

Terry's house from the high school  was 7.5 miles away

Speed of cars =  S km/hr  & S + 10  km/hr

Distance covered in 30 mins = 1/2 hr   =  60 km

=> S(1/2) + (S + 10))(1/2)  =  60

=> S + S + 10 = 120

=> 2S = 110

=>  S = 55   km/hr

S + 10 = 65 km/hr

Each Covered Distance = 55* 1/2 = 27.5 km  & 65*1/2 = 32.5 km

Alloy = 118 kg

Silver = (10/100)118 = 11.8 kg

let say Silver added = S kg

then (25/100)(118 + S)  = 11.8  + S

=> 118 + S = 47.2 + 4S

=> 3S  = 70.8

=> S = 23.6

23.6 kg silver to be added  

Decaffine Coffee  = D

50% Caffine Coffee = C

Caffine  =  0.5C

Total = D + C

(40/100)(D + C) =  0.5C

=> 4D + 4C = 5C

=> 4D = C

=> D/C   =  1/4

1 : 4  

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