Question

Two tailors, Valentina and Laura, sit down to do some embroidery. Valentina can embroider 2 shirts per hour, and Laura can get through 3 shirts per hour. In addition, the tailors had previously finished some shirts. Valentina has already completed 15 shirts, and Laura has completed 11 shirts. Valentina and Laura decide to take a break when they have finished the same total number of shirts. How many shirts, in total, will each tailor have finished? How long will that take?

Answer 1

Valentina and Laura finished the same total number of shirts in
`4` hours.

Total number of shirts finished by Valentina
`=23`

Total number of shirts finished by Laura
`=23`

Explanation:

Suppose that Valentina and Laura finished the same total number of shirts in
`t` hours.

Valentina can embroider 2 shirts per hour and Valentina has already completed 15 shirts.

Total number of shirts finished by Valentina
`=2t+15`

Laura can get through 3 shirts per hour and Laura has completed 11 shirts.

Total number of shirts finished by Laura
`=3t+11`

Therefore,

`2t+15=3t+11\\3t-2t=15-11\\t=4`

So,

Valentina and Laura finished the same total number of shirts in
`4` hours.

Total number of shirts finished by Valentina
`=2(4)+15=8+15=23`

Total number of shirts finished by Laura
`=3(4)+11=12+11=23`