Question

Juno ams Akima are training for a blathlon together. They are going to jog for the same amount of time as each other every day we are also going to bike for the same amount of time as each other do you know jogs at a rate of 6 miles and bikes at a rate of 14 miles he covers a total of 48 miles Akima jogs at a rate of 8 miles and bikes at the rate of 12 miles she covers a total of 44 miles how many hours does each one spend biking.

Answer 1

Answer:3 hours

Step-by-step explanation:

Juno jogs at rate of 6 miles and bikes at rate of 14 miles covering total of 48 miles.

Akima jogs at rate of 8 miles and bikes at rate of 12 miles covering total of 44 miles.

Let jogging be represented by j

Let biking be represented by b

For Juno, 6j + 14b = 48 ......... i

For Akima, 8j + 12b = 44.......... ii

Multiply equation I by 8

Multiply equation ii by 6

48j + 112b = 384 ........... iii

48j + 72b = 264 ............. iv

Subtract equation iv from iii

48j + 112b = 384

- 48j + 72b = 264

40b = 120

b = 120/40

b = 3

Number of hours spent biking is 3 hours.

Answer 2

Answer:

Step-by-step explanation:

Given:

Juno:

Biking rate, bj = 14 miles

Jogging rate, jj = 6 miles

Total distance, dj = 48 miles

Akimo:

Biking rate, ba = 12 miles

Jogging rate, ja = 8 miles

Total distance, da = 44 miles

Since they are going to jog for the same amount of time as each other every day we are also going to bike for the same amount of time as each other.

Rate, r = distance, d/time, t

Let t1 and t2 be the time taken for juno and akimo to jog and bike respectively.

Jogging:

Juno: 6t1

Akimo: 8t1

Biking:

Juno: 14t2

Akimo: 12t2

6t1 + 14t2 = 48

8t1 + 12t2 = 44

Solving the equations simultaneously,

t2 = (48 - 6t1)/14

Into the next equation,

8t1 + 12[(48 - 6t1)/14] = 44

t1 = 1 hour

Inputting t1 = 1 into t2 = (48 - 6t1)/14

t2 = 3 hours

Therefore, 3 hours is spent on biking.