勒罗伊看音乐剧迟到了 $\frac{1}{5}$ 小时。他观看了 1 小时 38 分钟，音乐剧于下午 3:15 结束。

1. Convert the time from hours to minutes

$\frac{1}{5} \text{ h} = \frac{1}{5} \times 60 \text{ min} = 12 \text{ min}$

1. Calculate the total duration of the musical

Leroy was $\frac{1}{5}\text{ h} = 12\text{ min}$ late.
Total duration of the musical = $1\text{ h } 38\text{ min} + 12\text{ min} = 1\text{ h } 50\text{ min}$

2. Subtract the total duration from the end time to find the start time

End time = $3.15\text{ p.m.}$
Start time = $3.15\text{ p.m.} - 1\text{ h } 50\text{ min}$
$3.15\text{ p.m.} - 1\text{ h} = 2.15\text{ p.m.}$
$2.15\text{ p.m.} - 50\text{ min} = 1.25\text{ p.m.}$