Math physics two questions, how do I......?

Question

John has a credit card from Bagel Bank and another from Arctic Bank. He has a total of $1,190 charged on his credit cards. Bagel Bank charges 15% simple interest per year and Arctic Bank charges 16% per year. The yearly interest charge John needs to pay is $183.90. How much money does John owe Bagel Bank before interest charges?

A cop was hidden behind a tree and clocked a Ford going by at forty-eight kph. 1/2 of an hour later, the cop clocked a Honda passing by at sixty-three kph. If the two cars continue at the same speed, how far will the Honda travel before it catchs up to the Ford?

Express as a decimal rounded to the tenths place.

Answer 1

Simultaneous equation

assume bank a and bank b

1190 = a + b

a x 0.15 + b x 0.16 = 183.9

so a + 1.0666666b = 1226

so 0.06666666b = 36

b = 540

a = 650

I think that makes Bagel bank balance -$ 540

and artic bank balance -$650

and to the other question 1hour 36mins, as the distance between them is 24KM and the speed difference is 15KMH that is 1.6 houirs (1hour 36mins)

Answer 2

<< John has a credit card from Bagel Bank and another from Arctic Bank. He has a total of $1,190 charged on his credit cards. Bagel Bank charges 15% simple interest per year and Arctic Bank charges 16% per year. The yearly interest charge John needs to pay is $183.90. How much money does John owe Bagel Bank before interest charges?>>

Let

A = amount John owes Arctic Bank

B = amount John owes Bagel Bank

Equation 1 --- He has a total of $1,190 charged on his credit cards.

A + B = 1190

Equation 2 --- Bagel Bank charges 15% simple interest per year and Arctic Bank charges 16% per year. The yearly interest charge John needs to pay is $183.90.

0.15B + 0.16A = 183.90

<< How much money does John owe Bagel Bank before interest charges? >>

From Equation 1, A = 1190 - B and substituting this into Equation 2,

0.15B + 0.16(1190 - B) = 183.90

0.15B + 190.4 - 0.16B = 183.90

Rearranging the above,

0.016B - 0.015B = 190.4 - 183.90

0.01B = 6.50

B = $650 --- this is how much John owes Bagel Bank before interest.

<< A cop was hidden behind a tree and clocked a Ford going by at forty-eight kph. 1/2 of an hour later, the cop clocked a Honda passing by at sixty-three kph. If the two cars continue at the same speed, how far will the Honda travel before it catchs up to the Ford?

Express as a decimal rounded to the tenths place.>>

Let

F = distance travelled by Ford

H = distance travelled by Honda

F = 48(Tf)

H = 63(Th)

where

Tf = travel time of Ford

Th = travel time of Honda

Tf = Th + 0.5, therefore substituting (Th + 0.5) in the equation for F,

F = 48(Th + 0.5)

When the Honda catches up with the Ford,

F = H, therefore

48(Th + 0.5) = 63(Th)

48(Th) + 24 = 63(Th)

Solving for Th,

63Th - 48Th = 24

15Th = 24

Th = 1.6 hours

Therefore,

H = 63(1.6) = 100.8 km --- the distance that the Honda has to travel to catch up with the Ford.