Distance word problem

Question

Bharat and Ingrid leave their building at the same time on their bikes. If Bharats speed is 12 mph and Ingrid is 14 mph, how long will it take before they are 78 miles apart? If bharat rides a total of B miles, write an expression for how far Ingrid travels. Write two equations and solve. I can solve the system but I need the setup/equations.

Answer 1

FIRST STEP

The formula relating distance, speed and time is

Distance= speed × Time

(a) If Bharat rides a distance of b kilometers, then time taken by him to ride this distance is given by

Time = Distance/speed

=(b/12) hours

Now, with the speed 14 kilometers per hour Ingid can ride the distance in this time

Distance =speed × Time

=14 × b/12

=14b/12

=7b/6

(b) Let db represents the distance travelled by Bharat after any time in hours

db = 12 × t

Let di represents the distance travelled by Ingrid after any time t in hours.

di = 14×t

We need to find the time when the distance between them becomes 78 kilometers. We can represent this situation by the equation shown below.

di +dI = 78

SECOND STEP

We haveadded the di from d, because ingrid and Bharat are travelling in opposite direction and the distance between them is greater and greater after every instant. Now we need to substitute the values of di, and d, into di+d=78

14t +12t = 78

26t =78

t =78/26 (divided each side by 26)

t = 3 hours

Therefore, After 3 hours the distance between Bharat and Ingrid becomes 78 kilometers.

FINAL STEP

(a)7b/6

(b) After 3 hours the distance between Bharat and Ingrid becomes 78 kilometers.